FINANCE RESEARCH SEMINAR

SUPPORTED BY UNIGESTION

"TECHNOLOGICAL INNOVATION:

WINNERS AND LOSERS"

Prof. Leonid KOGAN MIT, Sloan School of Management

Abstract

We analyze the effect of innovation on asset prices in a tractable, general equilibrium

framework with heterogeneous households and firms. Innovation has a

heterogeneous impact on households and firms. Technological improvements

embodied in new capital benefit workers, while displacing existing firms and their

shareholders. This displacement process is uneven: newer generations of

shareholders benefit at the expense of existing cohorts; and firms well positioned to

take advantage of these opportunities benefit at the expense of firms unable to do so.

Under standard preference parameters, the risk premium associated with innovation

is negative. Our model delivers several stylized facts about asset returns,

consumption and labor income. We derive and test new predictions of our

framework using a direct measure of innovation. The model's predictions are

supported by the data.

Friday, September 27, 2013, 10:30-12:00 Room 126, Extranef building at the University of Lausanne

NBER WORKING PAPER SERIES

TECHNOLOGICAL INNOVATION:WINNERS AND LOSERS

Leonid KoganDimitris Papanikolaou

Noah Stoffman

Working Paper 18671http://www.nber.org/papers/w18671

NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts Avenue

Cambridge, MA 02138January 2013

Dimitris Papanikolaou thanks the Zell Center for Risk and the Jerome Kenney Fund for financial support.Leonid Kogan thanks J.P. Morgan for financial support. The views expressed herein are those of theauthors and do not necessarily reflect the views of the National Bureau of Economic Research.

NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies officialNBER publications.

© 2013 by Leonid Kogan, Dimitris Papanikolaou, and Noah Stoffman. All rights reserved. Short sectionsof text, not to exceed two paragraphs, may be quoted without explicit permission provided that fullcredit, including © notice, is given to the source.

Technological Innovation: Winners and LosersLeonid Kogan, Dimitris Papanikolaou, and Noah StoffmanNBER Working Paper No. 18671January 2013JEL No. E20,E32,G10,G12

ABSTRACT

We analyze the effect of innovation on asset prices in a tractable, general equilibrium framework withheterogeneous households and firms. Innovation has a heterogenous impact on households and firms.Technological improvements embodied in new capital benefit workers, while displacing existing firmsand their shareholders. This displacement process is uneven: newer generations of shareholders benefitat the expense of existing cohorts; and firms well positioned to take advantage of these opportunitiesbenefit at the expense of firms unable to do so. Under standard preference parameters, the risk premiumassociated with innovation is negative. Our model delivers several stylized facts about asset returns,consumption and labor income. We derive and test new predictions of our framework using a directmeasure of innovation. The model's predictions are supported by the data.

Leonid KoganMIT Sloan School of Management100 Main Street, E62-636Cambridge, MA 02142and NBERlkogan@mit.edu

Dimitris PapanikolaouKellogg School of ManagementNorthwestern University2001 Sheridan RoadEvanston, IL 60208and NBERd-papanikolaou@kellogg.northwestern.edu

Noah StoffmanKelley School of BusinessIndiana University1309 E 10th StreetBloomington, IN 47405nstoffma@indiana.edu

Introduction

The history of technological innovation is a story of displacement. New technologies emerge

that render old capital and processes obsolete. Further, these new technologies are typically

embodied in new vintages of capital, so the process of adoption is not costless. For instance,

the invention of the automobile by Karl Benz in 1885 required investment in new types

of capital, such as paved highways and an infrastructure for fuel distribution. Resources

therefore needed to be diverted into investment in the short run in order for the economy to

benefit in the long run. Not all economic agents benefitted from the automobile. Railroad

firms, which in the late 19th century accounted for 50% of the market capitalization of of all

NYSE-listed firms, were displaced as the primary mode of transport.1

We analyze the effect of innovation on the stock market using a general equilibrium model.

We model innovation as technological change embodied in new vintages of capital goods.2 A

key feature of innovation is that it leads to benefits and losses that are unevenly distributed.

Hence we consider an economy where both households and firms vary in their exposure to

innovation shocks. This heterogeneous impact differentiates innovation from disembodied

technical change – in our case a labor augmenting productivity shock – that affects equally

all vintages of capital goods.

Innovation leads to displacement of existing owners of capital and therefore to an in-

crease in the marginal utility of consumption of stock market participants. This process of

displacement occurs through two channels. First, innovation leads to wealth reallocation

between shareholders and workers. Innovation reduces the value of older vintages of capital.

In contrast, in our model, labor benefits from innovation since their skill is not tied to a

particular technology. As long as shareholders and workers do not fully share risks – for

instance, due to limited stock market participation by workers – aggregate innovation shocks

lead to wealth reallocation between the owners of capital and workers.

1Flink (1990, p. 360) writes: “The triumph of the private passenger car over rail transportation in theUnited States was meteoric. Passenger miles traveled by automobile were only 25 percent of rail passengermiles in 1922 but were twice as great as rail passenger miles by 1925, four times as great by 1929.”

2We use the terms innovation and capital-embodied change interchangeably in this paper. More precisely,we study a particular form of technological innovation, specifically innovation that is embodied in newvintages of intermediate goods. Accordingly, our empirical measure of embodied shocks relies on patent data,since innovation that is embodied in new products is more easily patentable (see, for example, Comin, 2008,for a discussion on patentable innovation). The type of innovation that we study could be related to theconcept of skill-biased technical change, but the two concepts are in general distinct. For instance, the firstindustrial revolution, a technological change embodied in new forms of capital – the factory system – ledto the displacement of skilled artisans by unskilled workers, who specialized in a limited number of tasks(see e.g. Sokoloff, 1984, 1986; Atack, 1987; Goldin and Katz, 1998). Further, skill-biased technical changeneed not be related to firms’ growth opportunities in the same manner as the embodied technical change weconsider in this paper.

1

Second, innovation results in reallocation of wealth across generations. Intergenerational

risk sharing is limited in our model. Households have finite lives; each new cohort of households

brings with it embodied technological advances in the form of blueprints. Only part of the

rents from innovation are appropriated by existing shareholders. Since households cannot

share risks with future generations, periods of significant innovation result in wealth transfer

from the existing set of households to the newer generations.

Firms have heterogenous exposure to innovation shocks, leading to cross-sectional dif-

ferences in risk premia. Firms that are able to capture a larger share of rent from the new

inventions benefit more from improvements in the frontier level of technology relative to

firms that are heavily invested in older vintages of capital. Since firms with high growth

opportunities are less susceptible to the displacive effect of innovation, they are a valued

highly by financial market participants, earning relatively low average returns in equilibrium.

This result is consistent with extensive empirical evidence on stock returns of growth firms.

Further, due to their similar exposure to the aggregate innovation shock, stock returns of

firms with similar access to growth opportunities comove with each other, above and beyond

of what is implied by their exposures to the market returns.

We calibrate our model to match several moments of real economic variables and asset

returns, including the mean and volatility of the aggregate consumption growth rate, the

equity premium, and the risk-free rate. Our main focus is on the model’s cross-sectional

predictions. Observable firm characteristics, such as valuation ratios or past investment rates,

are correlated with firms’ growth opportunities. This endogenous relation allows the model

to replicate several stylized facts about the cross-section of asset returns. Both in the data,

and in the model, firms with high market-to-book ratios or investment rates (growth) have

lower average returns than firms with low market-to-book ratios or investment rates (value).

Most importantly, our model captures the tendency of growth (or value) firms to comove

with each other, over and above their exposure to the market portfolio. Further, our model

replicates the failure of the CAPM and the consumption CAPM in pricing the cross-section

of stock returns, since neither the market portfolio nor aggregate consumption is a sufficient

statistic for the marginal utility of market participants.

We test the direct implications of our mechanism using a novel measure of embodied

technology shocks constructed in Kogan, Papanikolaou, Seru, and Stoffman (2012), which

infers the value of innovation from stock market reactions to news about patent grants.

The measure of Kogan et al. (2012) has a natural interpretation in the context of our

model; we construct this measure in simulated data and show that it is a close match to the

current real investment opportunity set in the economy. Armed with a proxy for the key

unobservable variable in our model, we concentrate our empirical analysis on the properties of

2

the model directly linked to its main economic mechanism – displacement in the cross-section

of households and firms generated by embodied innovation shocks.

Our empirical tests support the model’s predictions regarding household consumption and

innovation. First, innovation shocks generate displacement in the cross-section of households.

The level of technological innovation during the year when household heads enter the economy

is associated with higher lifetime consumption; by contrast, innovation shocks following

the cohort’s entry tend to lower its consumption level relative to the rest of the economy.

These patterns exist only for households that own stocks. Moreover, and consistent with

our model, higher innovation predicts lower consumption growth of stockholders relative to

non-stockholders.

Next, we relate the measure of innovation to firm outcomes. We find that firms with high

growth opportunities are displaced less than firms with low growth opportunities when their

competitors innovate. Similarly, growth firms have higher return exposure to embodied shocks

than value firms. We find that this difference in innovation risk exposures is quantitatively

sufficient to account for the observed differences in average returns among value and growth

firms in the data. We approximate the stochastic discount factor of our model using our

innovation series and data on total factor productivity or consumption. The point estimates

of the market price of innovation risk are negative and statistically significant, and most

importantly they are close in magnitude to the estimates implied by the calibrated general

equilibrium model.

Our work is related to asset pricing models with explicit production.3 Papers in this

literature construct structural models with heterogeneous firms and analyze the economic

sources of cross-sectional differences in firms’ systematic risk, with a particular focus on

understanding the origins of average return differences among value and growth firms. Most

of these models are in partial equilibrium (e.g., Berk, Green, and Naik, 1999; Carlson, Fisher,

and Giammarino, 2004; Zhang, 2005; Kogan and Papanikolaou, 2011), with an exogenously

specified pricing kernel. Some of these papers develop general equilibrium models (e.g. Gomes,

Kogan, and Zhang (2003)), yet most of them feature a single aggregate shock, implying that

the market portfolio conditionally spans the value factor. In contrast, our model features two

aggregate risk factors, one of them being driven by embodied technology shocks. Using an

empirical measure of embodied technical change, we provide direct evidence for the model

mechanism rather than relying only on indirect model implications.

General equilibrium models face additional challenges in replicating properties of asset

returns, since dividends and consumption are both endogenous (e.g., Rouwenhorst, 1995;

Jermann, 1998; Boldrin, Christiano, and Fisher, 2001; Kaltenbrunner and Lochstoer, 2010).

3For a recent review of this literature, see Kogan and Papanikolaou (2012a)

3

Equilibrium models with only disembodied shocks often imply that the aggregate payout

of the corporate sector is negatively correlated with consumption (e.g., Kaltenbrunner and

Lochstoer, 2010). In these models, the fact that firms cut dividends in order to invest

following a positive disembodied shock implies that dividends are less pro-cyclical than

consumption (see e.g., Rouwenhorst, 1995). In our setup, dividends are much more responsive

than consumption to the embodied shock, which helps the model generate realistic moments

for stock returns.

Our work is related to the growing literature on embodied technology shocks (e.g., Cooley,

Greenwood, and Yorukoglu, 1997; Greenwood, Hercowitz, and Krusell, 1997; Fisher, 2006;

Justiniano, Primiceri, and Tambalotti, 2010). Technology is typically assumed to be embodied

in new capital goods – new projects in our setting. Several empirical studies document

substantial vintage effects in the productivity of plants.For instance, Jensen, McGuckin, and

Stiroh (2001) find that the 1992 cohort of new plants was 50% more productive than the

1967 cohort in its entry year, controlling for industry-wide factors and input differences.

Further, our paper is related to work that explores the effect of technological innovation on

asset returns (e.g., Greenwood and Jovanovic, 1999; Hobijn and Jovanovic, 2001; Laitner and

Stolyarov, 2003; Kung and Schmid, 2011; Garleanu, Panageas, and Yu, 2012). The focus of

this literature is on exploring the effects of innovation on the aggregate stock market. We

contribute to this literature by explicitly considering the effects of heterogeneity in both firms

and households in terms of their exposure to embodied technology shocks.

The closest related work is Papanikolaou (2011), Garleanu, Kogan, and Panageas (2012)

and Kogan and Papanikolaou (2011, 2012b). Papanikolaou (2011) demonstrates that in

a general-equilibrium model, capital-embodied technology shocks are positively correlated

with the stochastic discount factor when the elasticity of intertemporal substitution is less

than or equal to the reciprocal of risk aversion. However, the price of embodied shocks

in his model is too small relative to the data. We generalize the model in Papanikolaou

(2011), allowing for both firm and household heterogeneity and imperfect risk sharing among

households. Our model delivers quantitatively more plausible estimates of the risk premium

associated with innovation, as well as additional testable predictions. Our model shares

some of the features in Garleanu et al. (2012), namely intergenerational displacement risk

and technological improvements embodied in new types of intermediate goods. We embed

these features into a model with capital accumulation, limited market participation, and a

richer, more realistic cross-section of firms. In addition, we construct an explicit empirical

measure of innovation shocks and use it to directly test the empirical implications of our

model’s mechanism. Last, our work is related to Kogan and Papanikolaou (2011, 2012b), who

analyze the effect of capital-embodied technical progress in partial equilibrium. The general

4

equilibrium model in this paper helps understand the economic mechanism for pricing of such

innovation shocks, and provides further insights into how these shocks impact the economy.

Our work is related to the literature emphasizing the role of consumption externalities

and relative wealth concerns for asset prices and equilibrium investment and consumption

dynamics (Duesenberry, 1949; Abel, 1990; Gali, 1994; Roussanov, 2010). Consistent with

the presence of consumption externalities, Luttmer (2005) provides micro-level evidence that

consumption of neighbouring households has a negative effect on self-reported happiness

measures. Further, preferences for relative wealth can arise endogenously. The model of

DeMarzo, Kaniel, and Kremer (2007) shares some of the same features of the simple model

in Section 1, in that incomplete markets gives rise to relative wealth concerns among agents.

In DeMarzo et al. (2007) the relative wealth concerns arises due to competition with existing

agents for future resources that are in limited supply. In our setting, relative wealth concerns

arise due to inter-generational displacement.

Our model replicates several stylized facts documented in the consumption-based asset

pricing literature. First, our model is consistent with the findings of Malloy, Moskowitz, and

Vissing-Jorgensen (2009) that the return differential between value and growth firms has

a relatively high exposure to the consumption growth of stockholders, especially at lower

frequencies. Second, our model is consistent with the evidence in Lustig and Van Nieuwerburgh

(2008) and Lustig, Van Nieuwerburgh, and Verdelhan (2008), who report that human wealth

– the present value of wages discounted using the stochastic discount factor implied by

absence of arbitrage – earns lower risk premia than financial wealth. In our model, embodied

innovation shocks raise equilibrium wages while reducing dividends on existing firms, resulting

in a low correlation between the growth of dividends and labor income and a lower risk

premium for human wealth. Last, our model is consistent with the recently reported empirical

evidence on the dynamics of income shares of financial and human capital in Lettau and

Ludvigson (2011).

1 A simple model

To illustrate the main intuition behind our mechanism, we first present a simple two-period

model. The economy consists of overlapping generations of capital owners and workers.

Capital owners have logarithmic preferences over consumption C0 and C1

U(C0, C1) = lnC0 + E0[lnC1]. (1)

5

Workers do not participate in the financial markets. There are two technologies available to

produce output, k ∈ {o, n}, each using old or new capital, respectively.

In the first period, only the old technology is available. Existing capital owners are

endowed with a unit of capital Ko that, along with labor Lo,t, can be used to produce output

in each period:

Yo,t = Kαo L

1−αo,t , t = 0, 1. (2)

For simplicity, we normalize the measure of workers and capital owners to unity in the first

period. In the second period, a measure µ of new workers and new capital owners enter the

economy. The new capital owners own the entire stock of new capital, Kn, which produces

output according to

Yn,1 = (ξKn)α L1−α

n,1 , (3)

where ξ is a positive random variable with unit mean: ξ > 0 and E[ξ] = 1. The random

variable ξ is the technology shock embodied in the new vintage of capital. A value of ξ > 1

implies that the new capital is more productive than the old. In contrast, the new workers

are identical to the old workers; labor can be freely allocated to either the old or to the new

technology.

In equilibrium, the allocation of labor between the old and the new technology depends

on the realization of the embodied shock ξ,

Lo,1 =1 + µ

1 + ξµand Ln,1 = ξµ

1 + µ

1 + ξµ. (4)

Because of the Cobb-Douglas production technology, equilibrium consumption of existing

capital owners is proportional to the output of the old technology. Since Lo,1 is decreasing in

ξ, so does the consumption growth of existing shareholders,

Co1

Co0

=

(1 + µ

1 + ξµ

)1−α

. (5)

Equation (5) illustrates the displacive effect of innovation on the owners of existing capital.

Unlike workers, who can supply labor to both the new and the old firms, the owners of old

capital do not benefit from the embodied shock ξ. Since they compete with the owners of

new capital in the market for labor, a positive innovation shock leads to lower consumption

for the owners of existing capital.

Now, suppose that a claim on the output of the new technology were available at time 0.

For simplicity, assume that this claim is on an infinitesimal fraction of the output of the new

technology, so that (5) still characterizes the consumption growth of the old capital owners.

6

Given the preferences of the existing households (1) and their consumption growth (5), the

difference between the realized return to the new and the old technology is

Rn1 −Ro

1 =

(ξ

E[ξ]− 1

) (1 + µ

1 + ξµ

)1−α

. (6)

Since the innovation shock ξ is embodied in new capital, a positive innovation shock ξ > 1 is

associated with a higher return of the new technology relative to the old.

Proposition 1 In equilibrium, the claim to the new technology has a lower expected return

than the claim to the old technology,

E[Rn1 ] < E[Ro

1].

Proof. Let f(ξ) =(

ξE[ξ]

− 1) (

1+µ1+ξµ

)1−α

. Since f ′′(ξ) < 0, Jensen’s inequality implies

E[f(ξ)] < f(E[ξ]) = 0

Proposition 1 summarizes the intuition behind the main results of the paper. In con-

trast to labor, capital is tied to a specific technology. Hence, technological improvements

embodied in new vintages of capital lower the value of older vintages. Imperfect inter- and

intra-generational risk sharing imply that innovation leads to high marginal utility states

for the owners of existing capital. Given the opportunity, owners of existing capital are

willing to own a claim to the new technology, and accept lower returns on average, to obtain

a hedge against displacement. Limited risk sharing across new and old capital owners, as

well as shareholders and workers is key for this result. As a result of limited risk sharing,

the consumption CAPM fails in the model because the consumption growth of the marginal

investor (5) differs from aggregate, per capita, consumption growth

C1

C0

=

(1 + ξµ

1 + µ

)α

. (7)

The model in this section is too stylized to allow us to quantify the importance of this

mechanism of asset returns and economic quantities. Next, we develop a dynamic general

equilibrium model that builds on these basic ideas.

2 The model

In this section we develop a dynamic general equilibrium model that extends the simple model

above along several dimensions. First, we endogenize the investment in the capital stock each

period. Labor participates in the production of new capital, hence an increase in investment

7

expenditures leads to an increase in labor income. Labor benefits from the expansion and

improvement in the capital stock – as in the simple model above – but also because workers

do not share the costs of new capital acquisition with current capital owners. Second, the

model features a full cross-section of firms. Existing firms vary in their ability to capture

rents from new projects. By investing in existing firms, existing capital owners can hedge

their displacement from innovation. Differences in the ability of firms to acquire innovation

lead to ex-ante differences in risk premia. Third, we consider a richer class of preferences

that separate risk aversion from the inverse of the elasticity of intertemporal substitution

and allow for relative consumption effects in the utility function. These extensions allow for

a better quantitative fit of the model to the data, but do not qualitatively alter the intuition

from the simple model above.

2.1 Firms and technology

There are three production sectors in the model: a sector producing intermediate consump-

tion goods; a sector that aggregates these intermediate goods into the final consumption

good; and a sector producing investment goods. Firms in the last two sectors make zero

profits due to competition and constant returns to scale, hence we explicitly model only the

intermediate-good firms.

Intermediate-good firms

Production in the intermediate sector takes place in the form of projects. Projects are

introduced into the economy by the new cohorts of inventors, who lack the ability to

implement them on their own and sell these blueprints to existing intermediate-good firms.

There is a continuum of infinitely lived firms; each firm owns a finite number of projects. We

index individual firms by f ∈ [0, 1] and projects by j. We denote the set of projects owned

by firm f by Jf , and the set of all active projects in the economy by Jt.4

Active projects

Projects are differentiated from each other by three characteristics: a) their scale, kj, chosen

irreversibly at their inception; b) the level of frontier technology at the time of project

creation, s; and c) the time-varying level of project-specific productivity, ujt. A project j

4While we do not explicitly model entry and exit of firms, firms occasionally have zero projects, thustemporarily exiting the market, whereas new entrants can be viewed as a firm that begins operating its firstproject. Investors can purchase shares of firms with zero active projects.

8

created at time s produces a flow of output at time t > s equal to

yjt = ujt eξs kα

j , (8)

where α ∈ (0, 1), ξ denotes the level of frontier technology at the time the project is

implemented, and u is a project-specific shock that follows a mean-reverting process. In

particular, the random process governing project output evolves according to

dujt = θu(1− ujt) dt+ σu√ujt dZjt, (9)

All projects created at time t are affected by the embodied shock ξ, which follows a

random walk with drift

dξt = µξ dt+ σξ dBξt. (10)

The embodied shock ξ captures the level of frontier technology in implementing new projects.

In contrast to the disembodied shock x, an improvement in ξ affects only the output of new

projects. In most respects, the embodied shock ξ is formally equivalent to investment-specific

technological change.

All new projects implemented at time t start at the long-run average level of idiosyncratic

productivity, ujt = 1. Thus, all projects managed by the same firm are ex-ante identical

in terms of productivity, but differ ex-post due to the project-specific shocks. Last, active

projects expire independently at a Poisson rate δ.

Firm investment opportunities – new projects

There is a continuum of firms in the intermediate goods sector that own and operate projects.

Firms are differentiated by their ability to attract inventors, and hence initiate new projects.

We denote by Nft the Poisson count process that denotes the number of projects the firm

has acquired. The probability that the firm acquires a new project, dNt = 1, is firm-specific

and equal to

λft = λf · λft. (11)

The likelihood that the firm acquires a new project λft is composed of two parts. The

first part λf captures the long-run likelihood of firm f receiving new projects, and is constant

over time. The second component, λft is time-varying, following a two-state, continuous time

Markov process with transition probability matrix S between time t and t+ dt given by

S =

(1− µL dt µL dt

µH dt 1− µH dt

). (12)

9

We label the two states as {λH , λL}, with λH > λL. Thus, at any point in time, a firm can

be either in the high-growth (λft = λf · λH) or in the low-growth state (λft = λf · λL). The

instantaneous probability of switching to each state is µH dt and µL dt, respectively. Without

loss of generality, we impose the restriction E[λf,t] = 1. Our specification implies that the

aggregate rate of project creation λ ≡ E[λft] is constant.

Implementing new projects

The implementation of a new project idea requires new capital k purchased at the equilibrium

market price q. Once a project is acquired, the firm chooses its scale of production kj to

maximize the value of the project. A firm’s choice of project scale is irreversible; firms cannot

liquidate existing projects and recover their original costs.

Capital-good firms

Firms in the capital-good sector use labor to produce productive the investment goods needed

to implement new projects in the intermediate-good sector

It = ext LIt. (13)

The labor augmenting productivity shock x follows a random walk with drift

dxt = µx dt+ σx dBxt. (14)

Final-good firms

Final consumption good firms using a constant returns to scale technology employing labor

LC and intermediate goods Yt

Ct = Y φt (ext LCt)

1−φ . (15)

Production of the final consumption good is affected by the labor augmenting productivity

shock xt.

2.2 Households

There are two types of households, each with a unit mass: hand-to-mouth workers who supply

labor; and inventors, who supply ideas for new projects. Both types of households have finite

lives: they die stochastically at a rate µ, and are replaced by a household of the same type.

Households have no bequest motive and have access to a market for state-contingent life

10

insurance contracts. Hence, each household is able to perfectly share its mortality risk with

other households of the same cohort.

Inventors

Each new inventor is endowed with a measure λ/µ of ideas for new projects. Inventors are

endowed with no other resources, and lack the ability to implement these project ideas on

their own. Hence, they sell these projects to existing firms. Inventors and firms bargain over

the surplus created by new projects. Each inventor captures a share η of the value of each

project. After they sell their project, inventors invest their proceeds in financial markets.

Inventors are only endowed with projects upon entry, and cannot subsequently innovate. As

a result, each new successive generation of inventors can potentially displace older cohorts.

Inventors have access to complete financial markets, including an annuity market.

Inventor’s utility takes a recursive form

Jt = Et

∫ ∞

t

f(Cs, Cs, Js)ds, (16)

where the aggregator f is given by

f(C, C, J) ≡ ρ

1− θ−1

(C1−h

(C/C

)h)1−θ−1

((1− γ)J)γ−θ−1

1−γ

− (1− γ) J

. (17)

Household preferences depend on own consumption C, but also on the consumption of the

household relative to the aggregate C. Thus, our preference specification nests ‘keeping up

with the Joneses’ and non-separability across time (see e.g. Abel, 1990; Duffie and Epstein,

1992). The parameter h captures the strength of the external habit; ρ = ρ+ µ is the effective

time-preference parameter, which includes the adjustment for the likelihood of death µ; γ is

the coefficient of relative risk aversion; and θ is the elasticity of intertemporal substitution

(EIS).

Workers

Workers inelastically supply one unit of labor that can that can be freely allocated between

producing consumption or investment goods

LI + LC = 1. (18)

11

The allocation of labor between the investment-good and consumption-good sectors is the

mechanism through which the economy as a whole saves or consumes.

Workers are hand-to-mouth; they do not have access to financial markets and consume

their labor income every period.

3 Competitive equilibrium

Definition 1 (Competitive Equilibrium) The competitive equilibrium is a sequence of

quantities {CSt , C

Wt , Yt, LCt, LIt}; prices {pYt , pIt , wt}; firm investment decisions {kt} such that

given the sequence of stochastic shocks {xt, ξt, ujt, Nft}: i) shareholders choose consumption

and savings plans to maximize their utility (16); ii) intermediate-good firms maximize their

value according to (19); iii) Final-good and investment-good firms maximize profits; iv) the

labor market (18) clears; v) the market for capital clears (21); vi) the market for consumption

clears CSt + CW

t = Ct; vii) the resource constraints (13)-(15) are satisfied; and viii) market

participants rationally update their beliefs about λft using all available information.

We relegate the details of the computation of equilibrium to Appendix A.

3.1 Firm optimization

We begin our description of the competitive equilibrium by characterizing the firms’ optimality

conditions.

Market for capital

Intermediate good firms choose the scale of investment, kj, in each project to maximize its

net present value, that is, the market value of the new project minus its implementation

cost. We guess – and subsequently verify – that the equilibrium price of a new project equals

Pt eξt kα, where P is a function of only the aggregate state of the economy. Then, the net

present value of a project is

maxk

NPV = Pt eξt kα − pItk. (19)

The optimal scale of investment is a function of the ratio of the market value of a new project

to its marginal cost of implementation pIt ,

kt =

(α eξt Pt

pIt

) 11−α

. (20)

12

Equation (20) bears similarities to the q-theory of investment (Hayashi, 1982). A key difference

here is that the numerator involves the market value of a new project – marginal q – which

is distinct from the market value of the firm – average q. Aggregating across firms, the total

demand for new capital equals

It =

∫kft dNft = λ kt. (21)

The equilibrium price of investment goods, pIt , clears the supply (13) and the total demand

for new capital (21)

pIt = αeξt Pt

(λ

extLIt

)1−α

. (22)

A positive innovation shock leads to an increase in the demand for capital, and thus to an

increase in its equilibrium price pI .

Market for labor

Labor is used to produce both the final consumption good, and the capital needed to implement

new projects. The first order condition of the firms producing the final consumption good

with respect to labor input links their labor choice LC to the competitive wage wt

(1− φ)Y φt e(1−φ)xt L−φ

Ct = wt. (23)

The profit maximization in the investment-goods sector implies that

extpIt = wt. (24)

The equilibrium allocation of labor between producing consumption and investment goods

is determined by the labor market clearing condition (18), along with (22)-(24)

(1− φ)Y φt e(1−φ)xt (1− LIt)

−φ = α eα xt+ξt Pt

(λ

LIt

)1−α

. (25)

All else equal, an increase in the embodied shock ξ increases the demand for new investment

goods. As a result, the economy reallocates resources away from producing consumption

goods towards producing investment goods.

13

Market for intermediate goods

Consumption firms purchase the intermediate good Y at a price pY and hire labor LC at a

wage w to maximize their value. Their first order condition with respect to their demand for

intermediate goods yields

φY φ−1t (ext LCt)

1−φ = pYt . (26)

The price of the intermediate good pY is therefore pinned down by the equilibrium allocation

of labor to the final good sector LC and the supply of intermediate goods, Y .

The total output of the intermediate good, Yt, equals the sum of the output of the

individual projects, Yt =∫yf,t, and is equal to the effective capital stock

Yt = Kt ≡∫j∈Jt

eξj kαj dj. (27)

adjusted for the productivity of each vintage – captured by ξ at the time the project is

created – and for decreasing returns to scale. An increase in the effective capital stock K, for

instance due to a positive embodied shock, leads to a lower price of the intermediate good

and to displacement for productive units of older vintages.

3.2 Household optimization

Here, we describe the household’s optimality conditions.

Inventors

Upon entry, inventors sell the blueprints to their projects to firms and use the proceeds

to invest in financial markets. A new inventor entering at time t acquires a share of total

financial wealth Wt equal to

btt =ηλNPVt

µWt

, (28)

where NPVt is the maximand in (19), η is the share of the project value captured by the

inventor, and Wt is total financial wealth in the economy.

As new inventors acquire shares in financial wealth, they displace older cohorts. The

share of total financial wealth W held at time t by an inventor born at time s < t equals

bts = bss exp

(µ(t− s)− µ

∫ t

s

buu du

). (29)

Agents insure the risk of death with other members of the same cohort; hence surviving

14

agents experience an increase in the growth rate of per-capital wealth equal to probability of

death µ.

We guess – and subsequently verify – that the value function of an inventor born in time

s is given by

Jts =1

1− γb1−γts Ft, (30)

where Ft is a function of the aggregate state.

Even though the model features heterogenous households, aggregation is simplified due

to homotheticity of preferences. Existing inventors vary in their level of financial wealth,

captured by bts. However, all existing agents at time t share the same growth rate of

consumption going forward, as they share risk in financial markets. Hence, all existing

inventors have the same intertemporal marginal rate of substitution

πs

πt

=exp

(∫ s

t

fJ(Cu, Cu, Ju) du

)fC(Cs, Cs, Js)

fC(Ct, Ct, Jt), (31)

where J is the utility index defined recursively in equation (16), and f is the preference

aggregator defined in equation (17). We also refer to πs/πt as the stochastic discount factor.

Workers

Workers inelastically supply one unit of labor and face no investment decisions. Every period,

they consume an amount equal to their labor proceeds

CWt = wt. (32)

3.3 Asset prices

The last step in characterizing the competitive equilibrium involves the computation of

financial wealth. Since firms producing capital goods and the final consumption good have

constant returns to scale technologies and no adjustment costs, they make zero profits in

equilibrium. Hence, we only focus on the sector producing intermediate goods.

Total financial wealth is equal to the sum of the value of existing assets plus the value of

future projects

Wt = V APt + PV GOt. (33)

The value of financial wealth also corresponds to the total wealth of inventors, which enters

the denominator of the displacement effect (28). Next, we solve for the two components of

financial wealth.

15

Value of Assets in Place

A single project produces a flow of the intermediate good, whose value in terms of consumption

is pY,t. The value, in consumption units, of an existing project with productivity level ujt

equals

Et

[∫ ∞

t

e−δ s πs

πt

pY,s uj,s eξjkα

j ds

]=eξj kα

j

[Pt + Pt(uj,t − 1)

], (34)

where Pt and Pt are functions of the aggregate state of the economy – verifying our conjecture

above. The total value of all existing projects is equal to

V APt ≡∫j∈Jt

eξj kαj

[Pt + Pt(uj,t − 1)

]dj = Pt Kt, (35)

where K is the effective capital stock defined in equation (27).

Value of Growth Opportunities

The present value of growth opportunities is equal to the present value of rents to existing

firms from all future projects

PV GOt ≡(1− η)Et

∫ ∞

t

(∫λfs

πs

πt

NPVs df

)ds = λ(1− η)

[ΓLt +

µH

µL + µH

(ΓHt − ΓL

t

)](36)

where NPVt is the equilibrium net present value of new projects in (19), 1− η represents the

fraction of this value captured by existing firms; µH/(µH + µL) is the measure of firms in the

high growth state; and ΓLt and ΓH

t determine the value of a firm in the low- and high-growth

phase, respectively.

3.4 Dynamic evolution of the economy

The current state of the economy is characterized by the vector Zt = [χt, ωt], where

χ ≡ (1− φ)x+ φ logK (37)

ω ≡ αx+ ξ − logK. (38)

The dynamic evolution of the aggregate state Z depends on the laws of motion for ξ and

x, given by equations (10) and (14), respectively, and the evolution of the effective stock of

16

capital,

dKt =(i(ωt)− δ

)Kt dt, where i(ωt) ≡ λ eξtkt

α = λ eωt

(LIt

λ

)α

. (39)

At the aggregate level, our model behaves similarly to the neoclassical growth model.

Growth – captured by the difference-stationary state variable χ – occurs through capital

accumulation and growth in the level of labor-augmenting technology x. The effective capital

K grows by the average rate of new project creation λ, the equilibrium scale of new projects

k, and improvements in the quality of new capital ξ; the effective capital depreciates at the

rate δ of project expiration.

The variable ω captures transitory fluctuations along the stochastic trend. Since i′(ω) > 0,

an increase in ω accelerates the growth rate of the effective capital stock, and thus the

long-run growth captured by χ. We therefore interpret shocks to ω as shocks to the investment

opportunity set in this economy; the latter are affected both by the embodied innovation

shocks dξt and the disembodied productivity shocks dxt. Further, the state variable ω is

mean-reverting; an increase in ω leads to an acceleration of capital accumulation K, in the

future ω reverts back to its long-run mean. In addition to i(ω), the following variables in

the model are stationary since they depend only on ω: the optimal allocation of labor across

sectors LI and LC ; the consumption share of workers Cw/C; the rate of displacement of

existing shareholders b.

4 Model implications

Here, we calibrate our model and explore its implications for asset returns and aggregate

quantities. We then analyze the main mechanisms behind the model’s predictions.

4.1 Calibration

The model has a total of 18 parameters. We choose these parameters to approximately match

a set of aggregate and cross-sectional moments.

We choose the mean growth rate of the technology shocks, µx = 0.023 and µξ = 0.005, to

match the growth rate of the economy; and their volatilities σx = 0.05 and σξ = 0.125 to

match the volatility of shareholder consumption growth and investment growth, respectively.

We select the parameters of the idiosyncratic shock, σu = 1.15 and θu = 0.05, to match the

persistence and dispersion in firm output-capital ratios.

We choose the returns to scale parameter at the project level α = 0.45 to approximately

17

match the correlation between investment rate and Tobin’s Q. We choose a depreciation

rate of δ = 0.05 in line with typical calibrations of RBC models. We choose the share of

capital in the production of final goods φ = 0.3 to match the average level of the labor share.

The firm-specific parameter governing long-run growth rates, λf is drawn from a uniform

distribution [5, 15]; the parameters characterizing the short-run firm growth dynamics are

λH = 4.25, µL = 0.2 and µH = 0.05. We choose these values to approximately match the

average investment-to-capital ratio in the economy as well as the persistence, the dispersion

and the lumpiness in firm investment rates.

We choose a low value of time preference ρ = 0.005, based on typical calibrations. We

select the coefficient of risk aversion γ = 45 and the elasticity of intertemporal substitution

θ = 0.6 to match the level of the premium of financial wealth and the volatility of the risk

free rate. Our choice of the EIS lies between the estimates reported by Vissing-Jorgensen

(2002) for stock- and bondholders (0.4 and 0.8 respectively). We choose the preference weight

on relative consumption h = 1/2 following Garleanu et al. (2012), so that households attach

equal weights to own and relative consumption. Our calibration of relative consumption

preferences effectively halves the effective risk aversion with respect to shocks that have

symmetric effects on household and aggregate consumption. The degree of intergenerational

risk-sharing is affected by the bargaining parameter η; we calibrate η = 0.8 to match the

volatility of cohort effects. We choose the probability of death µ = 0.025, so that the average

length of adult life is 1/µ = 40 years. We create returns to equity by levering financial wealth

by 2, which is consistent with estimates of the financial leverage of the corporate sector (see

e.g. Rauh and Sufi, 2011).

4.2 Model properties

We start by verifying that our model generates implications about macroeconomic quantities

that are consistent with the data. Next, we study the implications of our model for asset

returns.

Quantities

The model generates realistic moments for aggregate quantities, in addition to the moments

we target, as we see in Table 1. Given that the standard RBC model does a reasonable job

replicating the behavior of aggregate quantities, we focus our attention on the implications of

the non-standard features of our setup relative to the standard RBC model.

The presence of the two aggregate technology shocks – embodied and disembodied –

results in a correlation between investment and consumption growth that is substantially less

18

than one (45%), which is in line with the data (44.1%). Limited stock market participation

typically implies that shareholder consumption is more volatile than aggregate consumption.

In our case, this is true, but the difference is quantitatively minor (3.7% vs 3.0%), which

is in line with the data (3.6% vs 2.8%). Hence, the improved performance of our model in

matching asset pricing moments is not a result of higher consumption volatility for financial

market participants.

Last, aggregate payout to capital owners – dividends, interest payments and repurchases

minus new issuance – are volatile and positively correlated with consumption and labor

income (51% and 30% respectively). Obtaining estimates of this number is complicated by

difficulties in measuring total payout; however, these numbers are in line with the documented

properties of dividends in Bansal and Yaron (2004).

Equity premium and the risk-free rate

The equity premium implied by our model is in line with the data, and realized equity returns

are sufficiently volatile. The risk-free rate is smooth, despite the relatively low EIS and the

presence of consumption externalities. The level of the risk-free rate is somewhat higher than

the post-war average, but lower than the average level in the long sample in Campbell and

Cochrane (1999).

We conclude that our model performs at least as well as most general equilibrium models

with production in matching the moments of the market portfolio and risk-free rate (e.g.,

Jermann, 1998; Boldrin et al., 2001; Kaltenbrunner and Lochstoer, 2010).

Cross-section of stock returns

The finance literature has extensively documented the value premium puzzle, that is, the

finding that firms with high book-equity to market-equity ratios (value) have substantially

higher average returns than firms with low book-to-market (growth) (Fama and French,

1992, 1993; Lakonishok, Shleifer, and Vishny, 1994). This difference in average returns is

economically large, and is close in magnitude to the equity premium. The book-to-market

ratio is closely related to the inverse of Tobin’s Q, as it compares the replacement cost of the

firm’s assets to their market value.5 A closely related finding is that firms with high past

investment have lower average returns than firms with low past investment (Titman, Wei,

and Xie, 2004).

5The difference arises because i) firms are also financed by debt; ii) the denominator in measures ofTobin’s Q is the replacement cost of capital rather than the book-value of assets. Nevertheless, Tobin’s Qand book-to-market generate very similar dispersion in risk premia.

19

Previous work has argued that growth firms have higher exposure to embodied shocks

than value firms (e.g. Papanikolaou, 2011; Kogan and Papanikolaou, 2010); hence studying

this cross-section in the context of our model is informative about the properties of embodied

shocks. We follow the standard empirical procedure (see e.g. Fama and French, 1993) and

sort firms into decile portfolios on their I/K and B/M ratios in simulated data. Table 2 shows

that our model generates a 5.9% spread in average returns between the high-B/M and the

low-B/M decile portfolios, compared to 6.4% in the data. Similarly, the model generates

difference in average returns between the high- and low-investment decile portfolios is −5.9%,

compared to −5.3% in the data.

An important component of the value premium puzzle is that value and growth firms

appear to have the roughly the same systematic risk, measured by their exposure to the

market portfolio, implying the failure of the Capital Asset Pricing Model (CAPM). Here, we

show that our model replicates this failure. As we see in Table 3, firms’ market betas are only

weakly correlated with their book-to-market ratios, and returns on the high-minus-low B/M

portfolio have a positive alpha with respect to the CAPM (3.6% in the model versus 5.9%

in the data). Similarly, CAPM betas are essentially unrelated to the firms’ past investment

rates in the model, and high-minus-low I/K portfolio has a CAPM alpha of -5.01%, compared

to -7.09% in the data.

Last, our model also replicates the fact that the high-minus-low B/M and investment rate

portfolios are not spanned by the market return, as evidenced by the low R2 resulting from

regressing their returns on the market return. This empirical pattern led Fama and French

(1993) to propose an empirical asset pricing model that includes a portfolio of value minus

growth firms as a separate risk factor in the time-series of returns, in addition to the market

portfolio. Our general equilibrium model provides a theoretical justification for the existence

of this value factor.

4.3 Inspecting the mechanism

Here, we detail the intuition behind the main mechanism in our model. We first consider

the mechanism for how innovation risk is priced – the relation between the innovation shock

and the stochastic discount factor. Then, we discuss the determinants of the cross-sectional

differences in exposure to innovation risk among firms, and the resulting differences in

expected stock returns.

20

Equilibrium quantities

Aggregate quantities show different responses to the embodied and disembodied shock. In

Figures 1 and 2 we plot the impulse response of consumption, investment, aggregate payout

and labor income to a positive embodied and disembodied shock respectively.

A positive embodied shock leads to an improvement in real investment opportunities.

Investment increases on impact – leading to an acceleration in capital accumulation – and

then reverts to a slightly lower level as the economy accumulates more capital. Aggregate

payout by firms declines on impact, as firms cut dividends or raise capital to fund investment

in new projects. Since the economy reallocates resources away from consumption towards

investment – as we see in panel a of Figure 3 – aggregate consumption drops on impact but

then sharply accelerates due to faster capital accumulation. Further, similar to the simple

model is section 1, a positive embodied shock increases the effective stock of capital K and

benefits laborers due to an increase in the equilibrium wage in the long run. In the extended

model, a positive innovation shock benefits workers relative to capital owners through an

additional channel: labor participates in the production of capital, hence equilibrium wages

also increase on impact.

In contrast, from the perspective of the existing shareholders, a positive embodied shock

leads to a much sharper drop in their consumption – and a much slower acceleration in future

consumption growth – relative to the aggregate economy, due to limited risk sharing with

workers and future generations. First, the increase in equilibrium wage leads to a temporary

reallocation of income from capital to labor, as we see in panel b of Figure 3. Second, the

embodied shock leads to displacement of existing cohorts by future generations of innovators,

which is captured by b(ωt) in panel c of Figure 3. Both of these effects imply that, in relative

terms, a positive embodied shock has a persistent negative impact on existing shareholders.

A positive disembodied shock leads to higher output in both the consumption and the

investment sector, leading to positive comovement in investment, consumption and output

growth. Further, as in the standard RBC model, dividends respond less then consumption

as firms cut payout to finance investment (see e.g. Rouwenhorst, 1995). Last, since the

disembodied shock affects the real investment opportunities ω, a positive disembodied shock

leads to a reallocation of wealth from existing shareholders to workers and future generations;

however, this effect is qualitatively minor.

Comparing the response of dividends to an embodied and disembodied shock, we see that

dividends respond more than consumption in the first case, and less than consumption in

the second case. Hence, the presence of the embodied shock is a key part of the mechanism

that leads to an equilibrium dividend process that is more pro-cyclical – with respect to

consumption – relative to existing models (e.g. Rouwenhorst, 1995; Kaltenbrunner and

21

Lochstoer, 2010).

Equilibrium price of technology shocks

The price of risk of technology shocks γi(ω) – which equals the sharpe ratio of a security

that is perfectly correlated with the shock – can be recovered from investors’ inter-temporal

marginal rate of substitution

dπt

πt

=− rft dt− γx(ωt) dBxt − γξ(ωt) dB

ξt . (40)

The equilibrium stochastic discount factor is proportional to the gradient of the utility

function of the stock holders in the model, therefore

dπt

πt

= [· · · ] dt− θ−1

(dCts

Cts

− h (1− θ)dCts

Cts

)− γ − θ−1

1− γ

dJtsJts

, (41)

At time t, the change in the marginal utility of consumption for an existing stockholder of

cohort s, s < t, is related to the change in her own consumption Ct; the change in aggregate

consumption Ct, due to relative consumption concerns parameterized by h; and the change

in continuation utility Jts. As a result, the price of risk of each technology shock γi depends

on how it affects each of these three objects.

In panel e of of Figure 3 we plot the conditional market price of innovation risk, γξ(ω).

The embodied shock is positively correlated with marginal utility; the price of innovation

risk is negative, and approximately equal to -0.8 at the mean of the stationary distribution of

ω. A positive embodied shock leads to lower instantaneous consumption growth for existing

shareholders, both in absolute as well as in relative terms, as we see in Figure 1, leading to

an increase in marginal utility. The effect of the embodied shock in the value function J is

in general ambiguous; following a positive embodied shock, shareholders capture a smaller

slice of a larger pie. The net effect on utility depends on preference parameters, including the

weight on relative consumption. In our calibration the displacement effect dominates, hence

the value function J of asset holders is negatively exposed to the innovation shock – panel d

of Figure 3 – resulting in a further increase in marginal utility following innovation.

The conditional market price of the disembodied shock γx(ω) is positive, and approximately

equal to 0.5 at the mean of the stationary distribution of ω, as we see in panel f of Figure 3.

The disembodied technology shock also affects the stochastic discount factor through several

channels. Some of these channels are the same as for the embodied shock. Since increased

labor productivity makes it cheaper to produce new capital, the disembodied shock also

affects real investment opportunities ω in (38). However, the key difference in comparison

22

to the embodied shock is that a positive disembodied technology shock also has a large

positive effect on consumption of stockholders, since increased labor productivity raises the

productivity of assets in place and future investments, as we see in Figure 2. This positive

effect dominates, hence the equilibrium price of risk of the disembodied shock is positive.

Firm risk premia

Equilibrium risk premia are determined by the covariance of stock returns with the equilibrium

stochastic discount factor. At the firm level, expected returns are heterogeneous because

firms have different exposures to technology shocks. Consider the decomposition of the firm

value in the intermediate-good sector:

Vft = V APft + PV GOft

=

∫j∈Jft

eξj kαj

[Pt + Pt(uj,t − 1)

]dj + λf (1− η)

[ΓLt + pft

(ΓHt − ΓL

t

)]. (42)

The first term captures the value of assets in place and depends on the firm’s current portfolio

of projects, Jf . The second term captures the value of growth opportunities. This term

depends on the current growth state of the firm, captured by the indicator function pft,

which equals one if the firm is in the high-growth state (λft = λH). Importantly, the

two components of the firm value, assets in place and growth opportunities, have different

exposures to technology shocks.

We derive the firms’ exposures to the fundamental shocks dBxt and dBξ

t from (42) using

Ito’s lemma:

dVft

Vft

=[· · · ] dt+ (1− φ)σx dBxt +Bft

(σξ dB

ξt + ασx dB

xt

), (43)

where

Bft =

(ζ ′ν(ωt) + ζ ′ν(ωt)

Avft

1 + Avft

)V APft

Vft

+

(ζ ′g(ωt) + ζ ′g(ωt)

Agft

1 + Agft

)PV GOft

Vft

, (44)

and ζν , ζg, ζν , and ζg are functions of the aggregate state of the economy ωt; the functions Avft

and Agft depend on the deviations of the firm’s project portfolio from the average productivity

(u = 1) and the firm’ growth state p = µH/(µH + µL) respectively.

The first stochastic term in (43), (1− φ)σx dBxt , is identical across firms, and is driven

solely by the disembodied productivity shocks. Variation in firm risk premia arises solely

due to the second term, Bft

(σξ dB

ξt + ασx dB

xt

), capturing firm exposures to unanticipated

23

changes in aggregate investment opportunities.

In Figure 5, we plot the firm’s innovation risk exposure Bf , as well as the innovation

exposure of each of the two firm value components, as functions of the firm’s state. We do

the same for the risk premia. The value of assets in place is negatively exposed to innovation

shocks, ζ ′ν(ω) < 0. The value of growth opportunities is less exposed to displacement, since

firms’ investment opportunities improve as a result of innovation. Hence, assuming the firm

is in its steady state average (Avf = 0, Ag

f = 0), the firm’s ratio of growth opportunities to

firm value PV GO/V is a primary determinant of the firm’s exposure to the embodied shock:

firms that derive larger fraction of their value from growth opportunities have higher loading

on the innovation shock, as we illustrate in panel a.

However, the firm’s ratio of growth opportunities to value, PV GO/V , is not a sufficient

statistic for the firm’s systematic risk. The firm’s current profitability Avf and current

investment opportunities, Agf , play a role. The timing of cash flows matters for risk exposures,

and firms’ idiosyncratic productivity shocks and their current growth state, λft, are transient

in nature. These firm-specific risk exposures are summarized by a firm specific exposure

that depends on the deviation from the average productivity (u = 1) and growth state

p = µH/(µH + µL). In panel b, we see that, holding the share of growth opportunities

constant, more productive firms have higher exposure to innovation shocks. Last, in panel

c, we see that firms with better current investment opportunities benefit disproportionately

more from aggregate innovation, hence ceteris paribus, Bf is increasing in λft. However, both

of these effects are qualitatively minor.

Risk exposure of human capital

In our calibrated model human capital earns lower risk premium than financial capital. This

lower risk premium results from the fact that labor income is positively correlated with the

embodied shock. As we show in Figure 1, a positive innovation shock leads to an increase in

the equilibrium wage and a decline in firm payouts and the level of financial wealth. This

prediction is consistent with existing evidence. In recent work, Lustig and Van Nieuwerburgh

(2008) and Lustig et al. (2008) document that returns to human wealth are lower than returns

to financial wealth. Lustig et al. (2008) calculate the risk premium of financial and human

wealth to be 3.77% and 2.17% respectively.

To facilitate a comparison with the results in Lustig and Van Nieuwerburgh (2008) and

Lustig et al. (2008), we define human capital in the model as the present value of aggregate

24

labor income,

Ht =Et

∫ ∞

t

πs

πt

ws ds. (45)

The ratio of human capital to total wealth H/(H + W ) in our benchmark calibration in

83%,which is close to the 90% ratio reported in Lustig et al. (2008). Our model implies that

the equilibrium risk premium on human capital is equal to 1.98%, compared to 4.11% for an

unlevered claim on the stock market.

The role of imperfect risk sharing

Three features of our model are non-standard relative to standard RBC models: a) limited

stock market participation by workers; b) limited intergenerational risk sharing; and c)

preferences over relative consumption. In this section, we explore the quantitative effect

of these features on the model’s predictions. In Table 10, we consider seven alternative

specifications of the model, where we switch off one or two of these features and summarize

the main properties of asset prices in the model.

We find that these three features have a minor effect on the behavior of aggregate

quantities. The first two moments of consumption growth are similar across specifications.

Further, the behavior of the risk-free rate and the volatility of stock returns are largely similar

across all the specifications. The major differences across specifications are in the equilibrium

prices of risk, which lead to different predictions for risk premia.

In columns “Alt 1” to “Alt 4” of Table 10, we summarize the key moments of the model

without relative-consumption effects in preferences. The version of the model with full stock

market participation and risk sharing across generations “Alt 1” produces a lower equity

premium relative to the benchmark model, 3.8% vs 8.3%. More importantly, the average

return on the value factor and its CAPM alpha are both negative and approximately equal to

-8%. Comparing specifications “Alt 2” and “Alt 3” to “Alt 4”, we see that both limited stock

market participation and limited intergenerational risk sharing are necessary to produce a

positive value premium. However, in this specification, the CAPM works quite well, since the

CAPM alpha of the value factor is close to zero.

As we see from column “Alt 5”, the relative-consumption feature of preferences does

not by itself generate the main properties of asset prices in the model. Without limited

risk sharing, the model with relative-consumption concerns produces a relatively low equity

premium of 3.1% and a negative value premium, -3.8%. In columns “Alt 6” and “Alt 7”, we

see that preferences over relative consumption magnify the effects of market incompleteness.

As we see in the last column of Table 10, relative consumption preferences ensure that the

25

CAPM fails in the model. Investors’ desire to hedge changes in relative consumption leads to

a version of the ICAPM (Merton, 1973).

In summary, the interaction of imperfect risk sharing and agents’ preferences is critical

for the cross-sectional asset pricing implications of the model – the value premium. In

contrast, even though the magnitude of the equity premium varies across specifications, it is

consistently positive. We conclude that the cross-section of asset returns is informative about

whether innovation leads to displacement of financial market participants.

5 Testing new empirical predictions

In this section we analyze the new testable predictions of the model that are directly tied to

its core economic mechanism.

5.1 Constructing a proxy for the embodied shock

Our empirical analysis relies on an observable measure of the state variable ω that captures

the state of real investment opportunities. We exploit the fact that, in the model, the total

net present value of new projects scaled by the aggregate stock market wealth, is a strictly

increasing function of the state variable ω,

At ≡1

Wt

∫NPVt dNft ∝ b(ωt), (46)

where b(ωt) = btt is the share of wealth captured by new inventors (28). As we see in panel A

of Figure 5, lnAt is almost a linear function of the state variable ω in the model.

In constructing our empirical proxy for (46), we use patents as the empirical equivalent to

the projects in our model economy. To assess their value, we use the methodology of Kogan

et al. (2012), who construct an estimate of the dollar value of patents granted to public firms

using their stock market reaction around the day that news of the patent issuance becomes

public. First, we obtain a dollar measure of innovation at the firm level, Avft, corresponding

to the net present value of all new projects created by firm f in year t. Second, we aggregate

across firms and scale by total market capitalization to obtain the empirical equivalent A of

(46). See Appendix B and Kogan et al. (2012) for more details on the empirical procedure.

To assess the effectiveness of the Kogan et al. (2012) procedure in the context of our

model, we replicate the construction of At in simulated data, defining the event day d as the

time when a firm acquires a new project. As we see in panel B of Figure 5, the innovation

measure At is highly correlated with the state variable ω, both in levels (93.4%) and in first

26

differences (80.1%). In terms of the primitive technology shocks, changes in lnAt in the

model are primarily driven by the innovation shock ξ; the median correlation between ∆ lnA

and ∆ξ and ∆x in simulated samples is 75.3% and 1.3% respectively.

We plot the aggregate innovation measure ln At in panel c of Figure 5. We see that this

measure of innovative activity lines up well with the three major waves of technological

innovation: the 1930s, consistent with the views expressed in Field (2003); the 1960s and

early 1970s – a period commonly recognized as a period of high innovation (e.g. Laitner and

Stolyarov, 2003); and the 1990s and 2000s.

In Table 4, we compare the properties of the innovation measure in the data and in the

model. First, we focus on the firm-level measure Av, scaled by the firm’s market capitalization

V . As we see in Panel A, both in the data and in the model, the cross-sectional distribution

of Av/V is highly skewed. Approximately half of the firms do not innovate, and most of the

innovative activity is concentrated in the right tail of the distribution. In Panel B, we see

that the relation between changes in the aggregate measure ln A and the stock market (or

Tobin’s Q) is negative and comparable in magnitude across the data and the model.

5.2 Innovation and consumption displacement

Here we test the model’s predictions about the relation between innovation and consumption.

Household-level evidence

Our model implies that the consumption of shareholders of cohort s, as a share of aggregate

consumption, equals

Cts

Ct

= b(ωs) exp

(µ(t− s)− µ

∫ t

s

b(ωu) du

)l(ωt). (47)

We estimate the empirical equivalent of equation (47) using data on non-durable household

consumption from the CEX. We define the household’s cohort as the year in which the head

of the household turns 25. Varying this age by plus or minus two years leads to similar results.

Absent measurement error, our innovation measure A is linearly related to b(ω), hence we

form the econometric specification by taking logs of both sides of (47)

lnCits − lnCt = β0 ln As + β1

t−1∑u=s+1

Au + β2 ln At + a(t) + c(t− s) + c2 Zi + εits (48)

where, i indexes households; t is the observation year; s is the cohort year; C denotes log

non-durable consumption expenditures; a(t) is a time trend; A is our innovation measure;

27

c(t − s) is a quadratic term parameterizing household age effects; and Zi is a vector of

household-level controls including years of education and number of earning members. We

cluster standard errors at the cohort level. We estimate (48) separately for stockholders and

non-stockholders.6 We include a deterministic time trend to account for the secular trend in

CEX data relative to aggregate consumption.

We focus on the coefficients β0, β1 and β2. The estimate of β0 captures the effect of

innovation on the consumption of the entering cohort – corresponding to the term b(ωs).

Our model implies that the coefficient β0 should be positive for stockholders. The estimate

of β1 captures the effect of displacement, which corresponds to the integral term inside the

exponential in (47). A higher level of innovation results in the displacement of stockholders

from earlier cohorts, hence our model predicts that β1 should be negative for stockholders.

Last, the coefficient β2 captures both the displacement of the stockholders from cohort

s by the time-t entrants and the contemporaneous consumption distribution between the

workers and the owners of capital. In the model, higher recent innovation results in a higher

consumption share of the workers. Thus, our model predicts that β2 should be negative for

stockholders and positive for non-stockholders.

The results in Panel I of Table 5 are consistent with the model. The coefficient β0 is positive

and statistically significant across specifications for both stockholders and non-stockholders,

suggesting that the level of technological innovation at the time households enters the market

has a lasting positive impact on their lifetime consumption. Consistent with our model,

the coefficient β1 is negative and statistically significant for stockholders, and statistically

insignificant for non-stockholders. Hence, our results imply that existing generations of

stockholders get displaced by subsequent innovation activity, while there is no corresponding

effect for non-stockholders. Last, the coefficient β2 is positive and statistically significant for

non-stockholders, but not significant for the stockholders.

As a robustness test, we repeat the exercise but we normalize by the mean consumption

level of stockholders in the CEX, rather than aggregate consumption. As we see in Panel II of

Table 5, results are similar. Relative to the total consumption of stockholders, consumption

of the stockholders from cohort s is positively affected by the innovation at the time of their

entry and negatively affected by subsequent innovation activity.

6We define stockholders as households that report owning stocks, bonds or mutual funds. Since manyhouseholds often do not report their bond and stock holdings in their retirement accounts, restricting thesample in this way is a conservative way of restricting the sample to stockholders.

28

Aggregate evidence

Here, we provide further supporting evidence using time series data on the consumption growth

rate of stockholders cS and non-stockholders cNS. We estimate the following specification,

(cSt+k − cSt

)−(cNSt+k − cNS

t

)= a+ β(T )∆ lnAt + εtT , (49)

where we study horizons from k = 1 to k = 4 years. We use the series constructed in Malloy

et al. (2009), which covers the 1982-2004 period.7 We compute Newey-West adjusted standard

errors in (49), setting the maximum number of lags equal to 3 plus the number of overlapping

years.

We show the empirical results in Panel A of Table 6. We find a negative relation

between our innovation measure and the consumption growth rate of stockholders relative to

non-stockholders. Despite the short length of the sample, the relation is statistically significant

at the 10% level at the one to three year horizon. To assess the economic magnitude of the

empirical estimates, we replicate the same procedure in simulated data. As we see in Panel

B, the empirical magnitudes are consistent with our calibrated model.

5.3 Innovation and firm displacement

Here, we test the prediction of the model that firms with few growth opportunities are more

vulnerable to displacement than firms with high growth opportunities.

Output

First, we show that consistent with the model, firms with high growth opportunities are less

subject to displacement by innovation activity of their competitors.8 To test this prediction,

we study the response of firm output – sales plus change in inventories – to the firm’s own

innovation activity, Af , and the innovation activity of its competitors, AIf ,

ln yft+k − ln yft = a0 + a1Aft + a2AIft + a3AIftD(Gft)H + b Zft + et+k, (50)

7We follow Jagannathan and Wang (2007) and construct annual consumption growth rates by usingend-of-period consumption. In particular, we focus on the sample of households that are interviewed inDecember of every year, and use the average 4 to 16 quarter consumption growth rate of non-stockholders,stockholders and top-stockholders, defined as in Malloy et al. (2009). Our results remain quantitatively similarwhen we instead construct annual growth rates by an equal-weighted average of the k-period consumptiongrowth of all households interviewed in year t.

8In the model, a positive innovation shock ξ leads to an increase in the total production of the intermediategood Y , and therefore a reduction in its price pY . Firms that did not innovate and thus extended theirproduction capacity will experience a reduction in sales. In the medium run, firms with high growthopportunities are less sensitive to this displacement effect because they are likely to acquire projects.

29

where y is firm output; Aft ≡ Avft

/Vft is innovation by the firm, scaled by its market

capitalization; AIft is a value-weighted average of innovation Aft by the firm’s competitors

(other firms in the same 3-digit SIC industry; D(G)H is a dummy variable taking the value

1 if the firm is ranked higher than the industry median in terms of growth opportunities –

proxied either by Tobin’s Q or by the investment rate. The vector of controls Z includes

industry effects; time effects; firm size; and lagged output growth. We examine horizons of

k = 1 to k = 7 years. To facilitate comparison between the data and the model, we scale the

variables Af and AIf to unit standard deviation. We cluster the standard errors by year.

As we see in Panel A of Table 7, innovation by competitors leads to displacement of firms

with low growth opportunities – measured either using Tobin’s Q or past investment – as

evidenced by the negative estimate of a2. In contrast, the interaction effect a3 is positive,

implying that firms with above-median growth opportunities are displaced less. This difference

in displacement is economically meaningful. A one-standard deviation increase in the amount

of innovation by firm’s competitors is associated with a 4.4-4.6% drop in output over the next

seven years for the firm’s that are below the median industry in terms of growth opportunities,

compared to 2.6-3.3% for the firms above the median. To assess the empirical magnitudes in

the context of our calibration, we replicate the analysis in simulated data from the model.

As we see in Panel B, the empirical magnitudes are close to those implied by the model.

Return exposure

Next, we show that differences in firm characteristics related to growth opportunities are

related to differences in firms’ exposures to the aggregate innovation shock. Using our

empirical measure of innovation A we study whether portfolios of stocks, sorted on either

their past investment rate, or their book-to-market ratio, have differential exposure to our

innovation measure A, controlling for their market exposure

Rpt − rft = ap + βp (Rmt − rft) + γp∆ ln At + εpt (51)

As we see in panel A of Table 8, firms with high (low) growth opportunities have positive

(negative) stock return exposure to innovation shocks ∆ lnAt, controlling for excess returns

to the stock market, Rmt − rft. The empirical magnitudes are comparable to the magnitudes

in simulated data, as we see in panel B.

30

5.4 Asset pricing tests

Having established that firms with different growth opportunities have differential return

exposure to our empirical proxy for the embodied shock, we use the cross section of asset

returns to test the model-implied relation between innovation and investors’ intertemporal

rates of substitution or stochastic discount factor (SDF). The SDF implied by the model (A.28)

is not available in analytic form, hence we estimate a linearized version

m = a− γx ∆x− γξ ∆ξ. (52)

We proxy for the innovation shock ∆ξ by changes in our log innovation measure ∆ ln A.

We proxy for the disembodied technology shock x by the change in the (log) total factor

productivity from Basu, Fernald, and Kimball (2006). In addition, since the disembodied

shock x accounts for most of the short-run variation in aggregate consumption growth, we

test an alternative version of the model where, we replace ∆x by aggregate consumption

growth.

We estimate (52) using the generalized method of moments (GMM), using the model

pricing errors as moment restrictions (Hansen and Singleton, 1982, 1983).9 As test assets,

we use deciles 1,2, 9 and 10 from the book-to-market and investment rate portfolios. We

report first-stage GMM estimates using the identity matrix to weigh moment restrictions,

and adjust the standard errors using the Newey-West procedure with a maximum of three

lags. As a measure of fit, we report the cross-sectional R2 and the mean absolute pricing

errors. We replicate the same procedure in simulated data.

The specifications of the stochastic discount factor without the innovation shock result in

large pricing errors, both in the data and in the model. As we see in columns A1 and A2 of

Table 9, differences in exposure with either total factor productivity or consumption growth

are not related to differences in risk premia across portfolios. In Panel B, we show that the

same pattern holds in simulated data. In particular, column B2 shows that the consumption

CAPM does not hold in the model, since there there is no relation between return exposures

to aggregate consumption growth and risk premia.

Specifications of the SDF with the innovation measure ∆ ln A do well in pricing these

portfolios, as we see in columns A3 and A4. The price of risk associated with innovation

ranges from −0.83 to −1.03 and is statistically significant at the 1% level. These estimated

9We impose that the SDF in equation (52) should price the cross-section of test asset returns in excess ofthe risk-free rate. Hence, the mean of the stochastic discount factor is not identified. Without loss of generality,we choose the normalization E(m) = 1, which leads to the moment restrictions E[Re

i ] = −cov(m,Rei ), where

Rei denotes the excess return of portfolio i over the risk-free rate (see Cochrane, 2005, pages 256-258 for

details.)

31

risk prices are very close to those implied by our calibrated model in columns B3 and B4,

which range from −1.01 to −1.15 across specifications. Last, both in the data and in the

model, the estimated price of the disembodied shock is γx is not statistically different from

zero, likely due to the lack of dispersion in x-shock exposures across portfolios. We conclude

that the relation between embodied shocks and intertemporal rates of substitution implied

by our calibrated model is quantitatively consistent with the data.

6 Conclusion

We develop a general equilibrium model to study the effects of innovation on asset returns.

A distinguishing feature of innovation is that its benefits are not shared symmetrically across

all agents in the economy. Hence, focusing on aggregate moments obscures the effects of

innovation in the cross-section of both firms and households. Specifically, technological

improvements embodied in new capital benefit workers employed in their production, while

displacing existing firms and their shareholders. This displacement process is uneven for two

reasons. First, newer generations of shareholders benefit at the expense of existing cohorts.

Second, firms well-positioned to take advantage of these opportunities benefit at the expense

of firms unable to do so. Existing shareholders value firms rich in growth opportunities

despite their low average returns, as they provide insurance against displacement.

Our model delivers rich cross-sectional implications about the effect of innovation on the

cross-section of firms and households that are supported by the data. We test the model’s

predictions using a direct measure of innovation constructed by Kogan et al. (2012) using

data on patents and stock returns. Consistent with our model, we find that innovation is

associated with a reallocation of wealth from existing shareholders to workers and future

generations.

Our work suggests several avenues for future research. Quantifying the impact of wealth

reallocation associated with innovation on inequality among households is a promising

direction for future work, especially given the availability of a direct measure of technology.

Another important topic to consider would be the role of government policies in mitigating

intergenerational displacement. Last, we only focus on one particular type of innovation, that

is technological change embodied in new capital. Analyzing the effects of more general types

of embodied technical change on financial markets and macroeconomy is potentially fruitful.

32

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36

Tables

Table 1: Calibration moments

A. Aggregate Quantities Model Data

Consumption growth, aggregate; mean∗ (%) 1.7 1.9Consumption growth, aggregate; standard deviation (%) 3.0 2.8Consumption growth, aggregate; serial correlation (%) 24.5 41.2Consumption growth, stockholders; standard deviation∗ (%) 3.7 3.6Dividend growth; standard deviation (%) 4.86 11.49Labor Income growth; standard deviation (%) 3.2 1.9Investment growth; standard deviation∗ (%) 11.6 14.8Investment to capital; mean∗ (%) 8.5 8.7Labor Share; mean∗ (%) 70.8 68.5Labor Share; standard deviation (%) 1.8 1.6First difference of consumption cohort effect, standard deviation∗ (%) 8.8 8.5Correlation between consumption and dividend growth (%) 50.6 55.0Correlation between consumption and investment (%) 45.0 44.1Correlation between consumption and stock market (%) 44.7 18.4

B. Asset returns Model Data

Market portfolio, excess returns; mean∗ (%) 8.0 7.6Market portfolio, excess returns; standard deviation (%) 12.0 18.5Risk-free rate; mean (%) 2.8 0.9-2.9Risk-free rate; standard deviation∗ (%) 0.7 0.9

C. Firm-level variables Model Data

Investment rate, IQR-to-Median∗ 1.19 1.21Investment rate, serial correlation∗ (%) 45.3 47.8Investment rate > 1, fraction of firm-year obs∗ (%) 1.3 1.4Tobin’s Q, IQR-to-Median 0.89 1.27Tobin’s Q, serial correlation (%) 90.4 79.5Correlation between investment and lagged Tobin’s Q∗ (%) 22.9 23.7Output to Assets, IQR-to-Median∗ 0.55 0.80Output to Assets, serial correlation∗ (%) 88.0 92.3

Starred moments are targeted in our calibration. Investment, capital and consumption data are from NIPA

over the 1926-2010 period; investment is non-residential private domestic investment; stock of capital is

current-cost from the NIPA Fixed Assets Table; consumption is non-durables plus services; nominal variables

are deflated by population and the CPI. Population is from the Census. Moments of shareholder consumption

growth are from the unpublished working paper version of Malloy et al. (2009) and includes adjustment

for measurement error. Correlation between dividends and consumption are from Bansal and Yaron (2004).

Moments of labor income are from Lustig et al. (2008). The volatility of consumption cohorts is computed as

in Garleanu et al. (2012), but we restrict the sample to households that are shareholders. Stock market data

are from CRSP. Firm-level accounting data are from Compustat. Labor share is constructed from Flow of

Funds data following Sekyu and Rios-Rull (2009). The moments of the real risk-free rate are from Campbell

and Cochrane (1999) and Bansal and Yaron (2004); the range refers to the pre- versus post-war sample.37

Table 2: Cross-section of expected returns

A. Data

B/M sort Lo 2 3 8 9 Hi Hi-Lo

E(R)− rf (%) 6.45 6.98 7.62 11.29 11.38 12.83 6.38(2.32) (3.18) (3.33) (4.00) (4.22) (3.90) (2.46)

σ(%) 21.38 17.64 17.74 22.01 21.38 25.74 20.43

I/K sort Lo 2 3 8 9 Hi Hi-Lo

E(R)− rf (%) 10.13 8.20 8.32 7.19 7.86 4.87 -5.26(3.42) (3.24) (4.03) (2.68) (2.40) (1.26) (-2.05)

σ(%) 23.52 20.19 17.37 21.01 25.50 28.93 17.11

B. Model

B/M sort Lo 2 3 8 9 Hi Hi-Lo

E(R)− rf (%) 4.15 5.53 6.57 9.04 9.31 10.01 5.86(3.61) (4.78) (5.48) (6.67) (6.74) (6.96) (7.74)

σ(%) 10.39 10.56 10.99 12.29 12.53 12.99 6.36

I/K sort Lo 2 3 8 9 Hi Hi-Lo

E(R)− rf (%) 8.67 7.28 6.16 5.97 4.86 2.79 -5.92(6.13) (5.57) (4.96) (4.45) (3.74) (2.21) (-11.49)

σ(%) 12.83 11.80 11.26 12.04 11.66 11.12 4.61

Table shows excess returns and standard deviation for portfolios sorted on two measures of growth opportunities:

book-to-market and past investment. Data is from CRSP/Compustat. Book to market is book value of common

equity divided by CRSP market capitalization in December. Investment rate is growth in property-pant and

equipment. Data period is 1950-2008. We form portfolios in June every year. We exclude financial firms

(SIC6000-6799), and utilities (SIC4900-4949). When computing investment rates and book to market in

simulated data, we measure the book value of capital as the historical cost of firm’s capital∑

Jftkjqτ(j) (τ(j)

denotes the time of creation of project j) divided by its current market value Vft.

38

Table 3: The failure of the CAPM

A. Data

B/M sort Lo 2 3 8 9 Hi Hi-Lo

α -1.51 0.11 0.87 3.74 4.03 4.35 5.86(-1.38) (0.16) (1.21) (2.44) (2.92) (2.20) (2.07)

βmkt 1.08 0.92 0.95 1.03 0.99 1.17 0.09(21.65) (22.91) (29.54) (8.95) (10.08) (11.14) (0.64)

R2 83.89 90.53 93.09 74.97 73.79 70.80 0.66

I/K sort Lo 2 3 8 9 Hi Hi-Lo

α 2.64 1.48 2.75 0.10 -0.60 -4.45 -7.09(1.85) (1.48) (2.39) (0.12) (-0.47) (-2.29) (-2.97)

βmkt 1.12 1.00 0.83 1.06 1.26 1.39 0.27(16.38) (17.79) (13.39) (21.26) (18.68) (16.5) (2.79)

R2 77.72 84.86 79.10 87.27 84.41 79.59 8.77

B. Model

B/M sort Lo 2 3 8 9 Hi Hi-Lo

α -2.33 -1.44 -0.77 0.60 0.74 1.26 3.55(-4.19) (-3.36) (-2.29) (3.44) (4.00) (5.17) (5.17)

βmkt 0.79 0.84 0.89 1.02 1.04 1.07 0.28(21.25) (28.23) (38.66) (79.78) (76.16) (61.12) (5.74)

R2 84.99 91.43 95.13 95.80 93.65 88.08 29.46

I/K sort Lo 2 3 8 9 Hi Hi-Lo

α 2.01 1.05 0.25 -0.43 -1.30 -3.03 -5.01(5.17) (3.56) (0.93) (-1.66) (-5.47) (-9.62) (-9.34)

βmkt 1.07 1.00 0.95 1.02 0.99 0.94 -0.14(36.53) (44.65) (42.45) (51.30) (53.62) (37.58) (-3.40)

R2 92.84 94.72 94.71 92.71 91.95 83.67 12.43

Table shows excess returns and standard deviation for portfolios sorted on two measures of growth opportunities:

book-to-market and past investment. See notes to Table 2 for details of the portfolio construction. Data for

the market portfolio and risk-free rate are from Kenneth French’s data library.

39

Table 4: Descriptive statistics of innovation measure

A. Moments of firm-level measure – Av/V

Model Data

Mean 0.044 0.029Standard deviation 0.129 0.05750-percentile 0.000 0.00075-percentile 0.024 0.01290-percentile 0.129 0.11395-percentile 0.250 0.14599-percentile 0.623 0.256

B. Moments of aggregate measure – ∆ ln A

Model Data

Standard deviation 8.57 33.22

Correlation with market excess returns -60.12 -55.40

Correlation with changes in Tobin’s Q -73.21 -57.63

Table compares descriptive statistics for our firm-level and aggregate innovation measure in the model and in

the data; Avft refers to the dollar value of innovation generated by firm f in year t; V refers to stock market

capitalization; A refers to the aggregate innovation measure. See Appendix B and Kogan et al. (2012) for

details. Sample period is 1950-2008.

40

Table 5: Innovation and consumption displacement

cits − ct

A. Stockholders

I. Relative to II. Relative tototal consumption group mean

lnAs 0.1600 0.0284 0.1613 0.0207(3.00) (2.22) (3.25) (1.71)∑t−1

u=s+1 Au -0.0606 -0.0588 -0.0597 -0.0374(-3.51) (-2.36) (-3.76) (-2.18)

lnAt 0.0357 0.0138(1.60) (0.91)

R2 0.128 0.265 0.052 0.185Observations 13787 12305 13787 12305

cits − ct

B. Non Stockholders

I. Relative to II. Relative tototal consumption group mean

lnAs 0.1640 0.0236 0.1834 0.0261(2.75) (2.22) (3.32) (2.48)∑t−1

u=s+1 Au -0.1311 -0.0023 -0.1255 0.0086(-7.58) (-0.13) (-7.83) (0.60)

lnAt 0.0769 0.0344(3.57) (3.07)

R2 0.208 0.317 0.132 0.226Observations 36050 29191 36050 29191

Time Trend Y Y - -Household controls - Y - Y

Table reports results of relating our innovation measure A to household consumption data (see equation (48)in main text). Household-level consumption data are from the CEX family-level extracts by Harris andSabelhaus (2000), available through the NBER website. Data covers the period 1980-2003. See Kogan et al.(2012) for details on the construction of A. Consumption is non-durables, defined as in Harris and Sabelhaus(2000). Stockholders are classified as households reporting ownership of stocks, bonds or mutual funds.Cohort age s is defined as the age the household turns 25. In panel I we normalize household consumption byper-capital aggregate consumption of non-durables. In Panel II we normalize by group (stockholder versusnon-stockolder) means. Depending on the specification, we include a vector of household controls whichcontains: linear and quadratic age effects; number of earning members; years of education. All specificationsin Panel I include a time trend to control for the secular trend in the CEX dataset. Standard errors areclustered by cohort.

41

Table 6: Innovation and stockholder consumption growth

A. Data(cSt+T − cSt

)−(cNSt+T − cNS

t

)T=1 T=2 T=3 T=4

∆ ln At -0.013 -0.026 -0.025 -0.029(-1.76) (-2.28) (-1.74) (-1.09)

R2 0.075 0.101 0.067 0.070

B. Model(cSt+T − cSt

)−(cNSt+T − cNS

t

)T=1 T=2 T=3 T=4

∆ ln At -0.022 -0.018 -0.017 -0.013(-2.14) (-1.73) (-1.23) (-0.98)

R2 13.36 3.28 2.23 1.97

Table reports results of relating our innovation measure A to the differential growth rate of stockholders vs

non-stockholders(cSt+T − cSt

)−(cNSt+T − cNS

t

)(see equation (49) in main text) in the data (Panel A) and the

model (Panel B). Sample period is 1980-2004. Standard errors are computed using Newey-West with T+1

lags. We standardize right-hand side variables to unit standard deviation.

42

Table 7: Innovation and firm displacement

A. Data

yt+T − yt T=1 T=2 T=3 T=4 T=5 T=6 T=7

i. Tobin’s Q

AIft -0.022 -0.026 -0.034 -0.035 -0.036 -0.038 -0.044(-3.84) (-2.21) (-2.92) (-2.66) (-2.62) (-2.67) (-3.10)

AIft ×D(Qft)H 0.010 0.010 0.019 0.018 0.013 0.015 0.019(2.79) (3.01) (6.23) (4.04) (2.59) (3.21) (2.54)

ii. Investment rate

AIft -0.020 -0.026 -0.032 -0.034 -0.039 -0.041 -0.046(-3.61) (-2.59) (-2.68) (-2.26) (-2.33) (-2.45) (-2.73)

AIft ×D(IKft)H 0.003 0.006 0.009 0.008 0.010 0.011 0.013(1.28) (1.63) (2.92) (1.98) (1.89) (2.05) (2.74)

B. Model

yt+T − yt T=1 T=2 T=3 T=4 T=5 T=6 T=7

i. Tobin’s Q

AIft -0.007 -0.012 -0.016 -0.020 -0.024 -0.027 -0.029(-2.19) (-2.30) (-2.50) (-2.66) (-2.83) (-2.90) (-2.93)

AIft ×D(Qft)H 0.002 0.005 0.009 0.013 0.017 0.021 0.024(2.38) (4.25) (5.58) (6.37) (6.69) (6.77) (6.68)

ii. Investment rate

AIft -0.012 -0.018 -0.022 -0.025 -0.028 -0.029 -0.030(-3.58) (-3.47) (-3.42) (-3.31) (-3.27) (-3.17) (-3.06)

AIft ×D(Ift)H 0.010 0.017 0.021 0.023 0.025 0.026 0.026(12.14) (10.33) (9.22) (8.40) (7.82) (7.36) (7.05)

Table presents results on the differential rate of firm displacement following innovation by competitors (AIf )depending on the firm’s measure of growth opportunities (Tobin’s Q or past investment rate). We estimateequation (50) in the data (Panel A) and in simulated data from the model (Panel B). Sample period is1950-2008. Accounting data are from Compustat; investment rate is growth rate in property, plant andequipment (ppegt); Tobin’s Q is CRSP market capitalization, plus book value of debt (dltt), plus book valueof preferred shares (pstkrv), minus deferred taxes (txdb) divided by book assets (at); output y is sales (sale)plus change in inventories (invt). We include a vector of controls Z containing industry effects; time effects;firm size; lagged output growth; and firm and industry stock returns. We cluster the standard errors by year.We scale the variables Af and AIf to unit 90-50 range and unit standard deviation respectively.

43

Table 8: Innovation and return comovement

A. Data

B/M sort Lo 2 3 8 9 Hi Hi-Lo

∆ lnAt 0.17 0.03 -0.03 -0.08 -0.12 -0.22 -0.39(4.49) (0.84) (-1.35) (-1.07) (-2.14) (-3.91) (-4.74)

Rmt − rf 1.21 0.94 0.92 0.97 0.90 0.99 -0.22(23.61) (21.98) (27.87) (7.33) (7.86) (9.24) (-1.58)

R2 86.87 90.65 93.23 75.61 75.46 74.40 18.69

I/K sort Lo 2 3 8 9 Hi Hi-Lo

∆ lnAt -0.13 -0.05 -0.04 0.09 0.17 0.12 0.25(-2.35) (-1.44) (-1.01) (2.03) (3.55) (1.75) (3.17)

Rmt − rf 1.02 0.96 0.80 1.13 1.40 1.49 0.47(14.07) (15.03) (13.48) (15.54) (17.26) (13.95) (4.33)

R2 79.15 85.22 79.42 88.18 86.66 80.46 19.16

B. Model

B/M sort Lo 2 3 8 9 Hi Hi-Lo

∆ lnAt 0.43 0.31 0.20 -0.07 -0.11 -0.17 -0.61(5.74) (5.32) (4.18) (-2.54) (-3.57) (-4.75) (-6.27)

Rmt − rf 0.96 0.96 0.97 0.99 1.00 1.01 0.05(22.83) (29.18) (36.59) (62.88) (60.24) (49.89) (0.92)

R2 89.50 93.68 96.07 98.89 98.85 98.49 54.33

I/K sort Lo 2 3 8 9 Hi Hi-Lo

∆ lnAt -0.17 -0.07 0.02 -0.06 0.03 0.21 0.38(-5.00) (-2.15) (0.62) (-2.07) (1.04) (4.59) (5.75)

Rmt − rf 0.99 0.99 0.98 1.00 1.00 0.99 -0.00(51.11) (54.84) (52.80) (60.31) (58.34) (40.34) (-0.01)

R2 98.52 98.65 98.48 98.87 98.72 97.05 44.98

Table relates our innovation measure A to stock returns of portfolios sorted on book to market (Part I) and

past investment (Part II). We estimate equation (51) in the data (Panel A) and in the model (Panel B).

Sample period is 1950-2008. See notes to Table 2 for details on portfolio construction. See main text and

Kogan et al. (2012) for details on the construction of A. Standard errors are computed using Newey-West

with 3 lags.

44

Table 9: Asset pricing tests

4 B/M + 4 I/K portfolios

FactorA. Data B. Model

(1) (2) (3) (4) (1) (2) (3) (4)

∆ lnXt 3.19 -0.54 0.69 -0.01[3.99] [-1.08] [4.22] [-0.76]

∆ lnCt 1.97 -0.92 0.88 0.11[3.70] [-1.02] [4.36] [0.89 ]

∆ lnA -0.83 -1.03 -1.01 -1.15[-3.64] [-3.88] [-6.90] [-6.52]

R2 -110.61 -63.68 64.70 74.61 -28.79 -8.57 82.77 81.96MAPE 3.10 2.53 1.06 1.00 2.86 2.45 0.86 0.87

Table presents results of estimating the stochastic discount factor implied by the model (equation (52) in main

text) in the data (Panel A) and in simulated data from the model (Panel B). Sample period is 1950-2008. See

notes to Table 2 for details on portfolio construction. See main text and Kogan et al. (2012) for details on the

construction of innovation measure A. Total factor productivity X is from Basu et al. (2006). Consumption

C is non-durables plus services from NIPA, deflated by CPI and population growth. Standard errors are

computed using Newey-West with 3 lags.

45

Tab

le10:Com

parativestatics

Calibration

(Alt1)

(Alt2)

(Alt3)

(Alt4)

(Alt5)

(Alt6)

(Alt7)

(Bench)

Lim

ited

stock

marketparticipation

--

YY

--

YY

Lim

ited

inter-generational

risk

sharing

-Y

-Y

-Y

-Y

Relativeconsumption

preferences

--

--

YY

YY

Con

sumption

grow

th,mean

1.75

1.74

1.73

1.72

1.73

1.72

1.72

1.71

Con

sumption

grow

th,volatility

3.13

3.07

3.01

3.01

3.02

3.02

3.01

3.02

Marketportfolio,meanexcess

return

3.75

8.04

4.07

12.57

3.10

6.99

4.65

8.07

Marketportfolio,volatility

10.63

13.50

16.59

13.79

10.03

11.27

12.75

11.98

Risk-freerate,mean

0.78

0.16

1.61

0.11

2.24

1.97

1.89

2.82

Risk-freerate,volatility

2.03

1.60

2.49

1.12

1.09

0.78

1.62

0.71

Valuefactor,mean

-7.79

-4.80

-3.66

2.92

-3.77

-1.04

-1.09

5.88

Valuefactor,CAPM

alpha

-8.57

-8.20

-4.34

-0.47

-2.94

-3.84

-1.97

3.54

Average

marketprice

ofdB

xt

2.12

2.04

1.97

1.57

1.10

1.01

0.86

0.51

Average

marketprice

ofdB

ξt

0.53

0.37

0.24

-0.49

0.30

0.13

-0.12

-0.78

Table

presents

comparativestatics

withrespectto

threeelem

ents

ofourmodel.Dep

endingonthecolumn,Alt1-A

lt7,weallow

forfullstock

market

participationbyworkers,fullintergen

erational

risk-sharing(b(ω

)=

1)an

dsetthepreference

weigh

ton

relative

consumption

tozero

(h=

0).In

each

case,wepresentmedianmom

entestimates

across

100simulation

s.Valuefactor

refers

tothedifference

inrealized

returnsbetweenthetopan

dbottom

book

-to-market

decileportfolio.

46

Figure

1:Resp

onse

toembodied

shock

a.Investment

b.Dividends

c.Lab

orincome

−5

05

1015

012345

years

logdeviationfromSSgrowth,%

−5

05

1015

−6

−4

−20

years

−5

05

1015

0

0.2

0.4

0.6

0.8

years

d.Con

sumption

,e.

Con

sumption

,existing

f.Con

sumption

,existing

aggregate

stockholders

stockholders(relativeto

total)

−5

05

1015

−0.20

0.2

0.4

0.6

years

logdeviationfromSSgrowth,%

−5

05

1015

−1

−0.50

years

−5

05

1015

−1

−0.50

years

E[ω]

E[ω]−

2σ[ω]

E[ω]+

2σ[ω]

Figure

plots

theim

pulserespon

seof

quan

tities

toaon

e-stan

darddeviation

increase

inthelevelof

theem

bodiedshock

ξ.Wecompute

impulserespon

ses

byfirstfixingasequence

ofstochasticshocks;

wethen

perturb

that

sequence

byaσξ

√∆tpositiveshock

to∆ξat

t=

0.Wedotheperturbationat

the

meanof

theergo

dic

distribution

ofω,as

wellas

atplus/minustw

ostan

darddeviation

s.Wesimulate

atmon

thly

frequencies,dt=

1/12.Werepeatthe

process

1,00

0times,an

daverage

theim

pulserespon

seacross

simulation

s.

47

Figure

2:Resp

onse

todisembodied

shock

a.Investment

b.Dividends

c.Lab

orincome

−5

05

1015

0

0.51

1.52

years

logdeviationfromSSgrowth,%

−5

05

1015

0

0.51

years

−5

05

1015

0

0.51

years

d.Con

sumption

,e.

Con

sumption

,existing

f.Con

sumption

,existing

aggregate

stockholders

stockholders(relativeto

total)

−5

05

1015

0

0.51

years

logdeviationfromSSgrowth,%

−5

05

1015

0

0.51

years

−5

05

1015

−1

−0.50

years

E[ω]

E[ω]−

2σ[ω]

E[ω]+

2σ[ω]

Figure

plots

theim

pulseresponse

ofquantities

toaone-standard

deviationincrease

inthelevel

ofthedisem

bodiedshock

x.Wecompute

impulse

responsesbyfirstfixingasequen

ceofstochastic

shocks;

wethen

perturb

thatsequen

cebyaσx

√∆tpositiveshock

to∆xatt=

0.Wedothe

perturbationatthemeanoftheergodic

distributionofω,aswellasatplus/minustw

ostandard

deviations.

Wesimulate

atmonthly

frequen

cies,

dt=

1/12.

Werepeattheprocess

1,00

0times,an

daverag

etheim

pulserespon

seacross

simulation

s.

48

Figure

3:M

odelSolution

−5

−4

−3

−2

0

0.050.1

0.150.2

ω

LI(ω)

a.labor

allocation

toI-sector

−5

−4

−3

−2

0.7

0.71

0.72

0.73

0.74

0.75

ω

w/Y

b.labor

shareof

output

−5

−4

−3

−2

0

0.51

1.52

ω

b(ω)

c.displacementrate

−5

−4

−3

−2

−30

−25

−20

−15

−10−5

ω

−logF

d.valuefunctionof

shareholders

−5

−4

−3

−2

−0.85

−0.8

−0.75

−0.7

−0.65

−0.6

ω

γξ(ω)

e.price

ofem

bodiedshock

−5

−4

−3

−2

0.450.5

0.550.6

0.65

ω

γx(ω)

f.price

ofdisem

bodiedshock

Figure

plots

thenumericalsolutionto

themodel

asafunctionofthestate

variable

ω.Weplotthesolutionin

therelevantrangeofωbasedonits

stationarydistribution

.

49

Figure

4:Firm

retu

rnsensitivityto

innovation

shock

00.2

0.4

0.6

0.8

1

−0.50

0.5

PVGO/V

a.Firm

exposure

toω

00.5

11.5

2−0.8

−0.6

−0.4

ut,firm

average

b.Exposure

ofVAP

λL

1λH

−0.20

0.2

0.4

λft

c.Exposure

ofPVGO

00.2

0.4

0.6

0.8

1

-0.020

0.02

0.04

0.06

PVGO/V

d.Firm

risk

premium

00.5

11.5

20.03

0.04

0.05

0.06

ut,firm

average

e.Riskpremium

ofVAP

λL

1λH

−0.04

−0.020

0.02

λft

f.Riskpremium

ofPVGO

E[ω]

E[ω]−

2σ[ω]

E[ω]+

2σ[ω]

Figure

plots

theexposure

ofthefirm

tochan

gesin

thestatevariab

leω

asafunctionof

itscharacteristics.

Weplotthesensitivityof

firm

valueto

ωas

afunctionoftheshare

ofgrowth

opportunitiesto

firm

value(panel

a),

asafunctionoftheshare

ofgrowth

opportunitiesto

firm

valuePVGO/V

assumingthat

thefirm

isin

itssteadystate:

(Av f=

0,A

g f=

0);thesensitivityof

assets

inplace

asafunctionof

theaverag

eproject-specificshock

atthefirm

level,u(pan

elb);an

dthesensitivityof

grow

thop

portunitiesas

afunctionof

thecu

rrentgrow

thstateof

thefirm

(pan

elc).In

pan

elsdto

fwecompute

conditional

risk

premia

bymultiply

firm

s’conditional

risk

exposuresto

xan

dξwiththeconditional

marketpricesof

risk

γx(ω

)an

dγξ(ω

).

50

Figure

5:M

easu

ringinnovation

a.Relativevalue

b.Innovationmeasure

c.Innovationmeasure

ofnew

projects

constructed

insimulateddata

(1927-2010)

−5

−4

−3

−2

−4

−3.5

−3

−2.5

ω

log((1−η)NPVt/Wt)

−5

−4

−3

−2

−3.6

−3.4

−3.2

−3

−2.8

ωlnA

1920

1940

1960

1980

2000

−4

−3

−2

−1

year

lnA

Inpan

elaweplotthevalueof

new

projects,

relative

tothestock

market,

asafunctionof

thestatevariab

leω.In

pan

elbwecomparetheinnovation

measure

ofKogan

etal.(2012)

constructed

insimulateddataversusrealizationsof

thestatevariab

leω

over

alongsimulation

of500years.

Inpan

elc

weplottheinnovationmeasure

ofKog

anet

al.(201

2)in

thedata.

51

A Analytical Appendix

In order to solve the fixed point problem, we conjecture that the equilibrium allocation of labor LI

is only a function of the stationary variable ω. We verify that this is indeed the case below.First, we characterize the consumption allocation. Workers consume their wage (see equa-

tion (32)), and shareholders consume the residual. Furthermore, all inventors have the sameconsumption-to-wealth ratio. As a result, the inventor’s share of financial wealth bts defined in (29)also determines the fraction of total consumption available to shareholders that he consumes

CSts = bts

(Ct − CW

t

)= bts e

χt

((1− LI(ω))

1−φ − (1− φ)(1− LI(ω))−φ), (A.1)

since

Ct =eχt(1− LI(ωt))1−φ (A.2)

we can write

C1−hts

(Cts

Ct

)h

= btse(1−h) χt l(ωt)

wherel(ω) ≡

(((1− LIt)

1−φ − (1− φ)(1− LIt)−φ))

(1− LI(ωt))−h(1−φ). (A.3)

Given the equilibrium consumption process A.1, the value function of an inventor born in time s isgiven by

Jts =1

1− γb(1−γ)ts e(1−γ)(1−h)χtf(ωt), (A.4)

where the function f satisfies the ODE

0 =ρ1− γ

1− θ−1l(ω)1−θ−1

f(ω)γ−θ−1

γ−1 + ρf (ω) f(ω) +Af(ω) (A.5)

where the operator A is defined as

Af(ω) ≡ f ′(ω)

(µξ + δ + αµx + (1− γ)(1− φ)ασ2

x − λeω(LI(ω)

λ

)α)+

1

2f ′′(ω)

(σ2ξ + α2 σ2

x

), (A.6)

and

ρf (ω) = −ρ(1− γ)

1− θ−1+ (1− γ) (µ− κ(ω)) + (1− h)(1− γ)

((1− φ)µx − φ δ + φλ1−αeωLI(ω)

α)

+1

2(1− φ)2σ2

x(1− γ)2(1− h)2. (A.7)

Given the consumption allocation (A.1) and the inventor’s value function (A.4), we compute the

52

stochastic discount factor,

πt = exp

(∫ t

0fJ(Cs, Cs, Js) ds

)fC(Ct, Ct, Jt),

where

hC,ts = ρ(eχt)−γ b−γts l(ωt)

−θ−1f(ωt)

γ−θ−1

γ−1 (A.8)

l(ωt) ≡(((

(1− LI(ωt))1−φ − (1− φ)(1− LI(ωt))

−φ))

(1− LI(ωt))−s(1−φ)

)θ−1

l(ωt) (A.9)

γ ≡ γ(1− h) + 1 (A.10)

hJ(C, J) = − ρ

1− θ−1

((γ − θ−1)

(l(ωt)

)1−θ−1

(f(ωt))1−θ−1

γ−1 + (1− γ)

). (A.11)

Next, we determine the value of assets in place and growth opportunities. First, we solve for thetwo functions P and P that determine the value of existing projects (34)

Pt = φ eχt K−1t

(l(ωt)

−θ−1f(ωt)

γ−θ−1

γ−1

)−1

ν(ωt) (A.12)

Pt = φ eχt K−1t

(l(ωt)

−θ−1f(ωt)

γ−θ−1

γ−1

)−1

ν(ωt), (A.13)

where ν(ω) and ν(ω) solve the ODEs

0 = (1− LI(ω))1−φ l(ω)−θ−1

f(ω)γ−θ−1

γ−1 + ρν(ω)ν(ω) +A ν(ω) (A.14)

0 = (1− LI(ω))1−φ l(ω)−θ−1

f(ω)γ−θ−1

γ−1 + (ρν(ω)− θu) ν(ω) +A ν(ω), (A.15)

and the function ρν is given by

ρν(ω) =− ρ

1− θ−1

((γ − θ−1)l(ωt)

1−θ−1f(ωt)

1−θ−1

γ−1 + (1− γ)

)+ γ(κ(ω)− µ)+

+((1− γ)φ− 1

)λ1−αeωLI(ω)

α + (1− h)(1− γ)((1− φ)µx − φδ) +1

2(1− γ)2(1− h)2(1− φ)2σ2

x.

(A.16)

Using (A.12) and (A.13), the value of a firm’s existing assets can be written as

V APft =φ eχt

(l(ωt)

−θ−1f(ωt)

γ−θ−1

γ−1

)−1

×

ν(ωt)∑j∈Jft

εξj kαj /Kt + ν(ωt)∑j∈Jft

εξj kαj (uj,t − 1) /Kt

. (A.17)

The relative contribution of the functions ν and ν in the value of assets in place depends on the sizeand profitability of existing projects, as we can see from the last term in (A.17). Second, we solve

53

for the two functions ΓH and ΓL that determine the value of growth opportunities

ΓHt =(1− α) eχt

(l(ωt)

−θ−1f(ωt)

γ−θ−1

γ−1

)−1 (g(ωt) + (λH − λL)

µL

µL + µHg(ωt)

)(A.18)

ΓLt =(1− α) eχt

(l(ωt)

−θ−1f(ωt)

γ−θ−1

γ−1

)−1 (g(ωt)− (λH − λL)

µH

µL + µHg(ωt)

)(A.19)

where g(ω) and g(ω) solve the ODEs

0 = ν(ω)eω(LI(ω)

λ

)α

+ ρg(ω) g(ω) +A g(ω) (A.20)

0 = ν(ω)eω(LI(ω)

λ

)α

+ (ρg(ω)− µL − µH) g(ω) +A g(ω), (A.21)

and the function ρg is given by

ρg(ω) ≡ρν(ω) + λ1−αeωLI(ω)α. (A.22)

Using (A.18)-(A.19) the value of the firm’s growth opportunities (36) equals

PV GOft =λf (1− η) (1− α) eχt

(l(ωt)

−θ−1f(ωt)

γ−θ−1

γ−1

)−1

×[g(ωt) +

(pft −

µH

µL + µH

)(λH − λL) g(ωt)

], (A.23)

so the contribution of the functions g and g to the value of growth opportunities depends on currentgrowth state of the firm pft. Aggregating (A.17) and (A.23) across firms, the aggregate value ofassets in place and growth opportunities is

V APt =φ eχt

(l(ωt)

−θ−1f(ωt)

γ−θ−1

γ−1

)−1

ν(ωt) (A.24)

PV GOt =λ (1− η)(1− α) eχt

(l(ωt)

−θ−1f(ωt)

γ−θ−1

γ−1

)−1

g(ωt). (A.25)

Given (A.24) and (A.25), we next determine the amount of inter-generational displacement

btt = b(ω) ≡λ η (1− α)φ ν(ω) eω

(LI(ω)

λ

)αφµ ν(ω) + λ µ (1− η)(1− α) g(ω)

. (A.26)

The last step is to determine the equilibrium allocation between the two sectors LI and verify thatit depends only on ω. The first order condition (25) simplifies to

(1− φ) (1− LI)−φ = αφ eωt

(l(ωt)

−θ−1f(ωt)

γ−θ−1

γ−1

)−1

ν(ωt)

(λ

LI

)1−α

. (A.27)

The competitive equilibrium involves the solution of the five differential equations (A.5), (A.14),(A.15), (A.20), (A.21) and the first order condition in (A.27). We solve for these equations usingfinite differences on a grid with 2,000 points.

We simulate the model at a weekly frequency dt = 1/52 and then aggregate the data to form

54

annual observations. We simulate 1,000 model histories of 3,000 firms and 120 years each. We dropthe first third of each history to eliminate the impact of initial conditions. When we compare theoutput of the model to the data, we report the median parameter estimate across simulations.

The equilibrium stochastic discount factor is given by

dπtπt

=− rft dt− γx(ωt) dBxt − γξ(ωt) dB

ξt , (A.28)

where γx(ω) =

[(γ (1− h) + 1) (1− φ) + α

(θ−1 l

′(ω)

l(ω)− γ − θ−1

γ − 1

f ′(ω)

f(ω)

)]σx,

γξ(ω) =

(θ−1 l

′(ω)

l(ω)− γ − θ−1

γ − 1

f ′(ω)

f(ω)

)σξ.

Last, the functions characterizing firm’s exposure to changes in aggregate growth opportunitiesare

ζν(ω) = ln

((l(ωt)

−θ−1f(ωt)

γ−θ−1

γ−1

)−1

ν(ω)

), ζν(ω) = ln

(ν(ω)

ν(ω)

), (A.29)

ζg(ω) = ln

((l(ωt)

−θ−1f(ωt)

γ−θ−1

γ−1

)−1

g(ω)

), ζg(ω) = ln

(g(ω)

g(ω)

), (A.30)

The functions Avft and Ag

ft depend on the current state of the firm,

Avft =

∑j∈Jft

eξj kαj (uj,t − 1)∑j∈Jft

eξj kαjeζν(ωt), and Ag

ft =

(pft −

µH

µL + µH

)(λH − λL) e

ζg(ωt). (A.31)

In our comparative statics, we allow for inter-generational risk sharing through the followingtransfer scheme: the social planner exchanges the financial wealth of entering cohorts with a fractionof the existing wealth in the economy µWt, implying that b(ω) = 1 always.

55

B Measurement Appendix

Aggregate quantities

Investment, capital and consumption data are from NIPA. Investment is non-residential privatedomestic investment; stock of capital is current-cost from the NIPA Fixed Assets Table; consumptionis non-durables plus services; nominal variables are deflated by population and the CPI. Populationis from the Census Bureau. We construct the labor share using Flow of Funds data followingSekyu and Rios-Rull (2009). We compute aggregate Tobin’s Q using NIPA and Flow of Funds datafollowing Laitner and Stolyarov (2003). Data on total factor productivity is from Basu et al. (2006).

We simulate the model at monthly frequencies and time-aggregate the data to form annualobservations. In simulated data, we measure consumption as the output of the consumption sectorC; we measure investment as the value of investment in terms of consumption units, pII; we measureoutput as the sum of consumption, investment and the inventors’ share of the net present value ofnew projects. When constructing aggregate Tobin’s Q, we measure the book value of capital as thehistorical cost of firm’s capital

∑Jft

kjqτ(j), where τ(j) denotes the time of creation of project j.

Innovation

We closely follow Kogan et al. (2012) in constructing the aggregate and firm-level innovation measure.The construction of the aggregate measure A proceeds in two steps. First, we infer the value of apatent based the stock market reaction around the day when a patent has been granted to a firm.We then aggregate our innovation measure across firms to infer the realizations of ω in the data.

We infer the value of patents from the stock market reaction around the day when a patent hasbeen granted to a firm. We decompose the idiosyncratic stock return r of firm f around the day dthat a patent is issued as

rfd = xfd + εfd, (B.1)

where xfd denotes the value of patent as a fraction of the firm’s market capitalization; and εfddenotes the component of the firm’s stock return that is unrelated to the intrinsic value of the patent.Following Kogan et al. (2012), we choose a three-day window over which we compute returns. Torecover the filtered value of the patent E[xfd|rfd], we follow the procedure of Kogan et al. (2012),which involves assumptions about the distribution of x and e, and use their estimated parameters.

We construct the conditional expectation of the dollar value of each patent j issued to firm f inday d as

Aj =1

PfdE[xfd|rfd] Vfd−1, (B.2)

where Vfd−1 is the market capitalization of the patenting firm on the day prior to the announcement.If multiple patents P are issued to the same firm on the same day, we assign each patent a fraction1/P of the total value.

To construct the firm-level measure of innovation, we aggregate the dollar values across allpatents on their grant and application days for firm f in year t:

Avft =

∑j∈Jft

Aj , (B.3)

where Jft denotes the sets of patents issued to firm f in year t. To avoid scale effects, we normalize

56

the dollar value of innovation (B.3) by the end-of-year firm market capitalization in year t,

Aft ≡Av

ft

Vft. (B.4)

To construct the aggregate measure of innovation, we aggregate the firm-level dollar measure (B.3)across the set Nt of firms in the entire economy, and scale by the sum of their end of year totalmarket capitalization S

At ≡∑

f∈NtAv

ft∑f∈Nt

Sft. (B.5)

We follow the same procedure in constructing (B.4) and (B.5) in simulated data.

Firm accounting data

Firm accounting data is from Compustat. Book to market is book value of common equity (ceq)divided by CRSP market capitalization in December. Investment rate is growth rate in property,plant and equipment (ppegt). Tobin’s Q is CRSP market capitalization, plus book value of debt(dltt), plus book value of preferred shares (pstkrv), minus deferred taxes (txdb) divided by bookassets (at). Output y is sales (sale) plus change in inventories (invt).

In simulated data, we measure the book value of capital as the historical cost of firm’s capital∑Jft

kjqτ(j), where τ(j) denotes the time of creation of project j; we measure firm investmentas the accumulated investment expenses over the year; we construct dividends as profits minusinvestment expenses minus payment to inventors for the acquisition of project blueprints.

Household consumption data

Data on household consumption is from the Consumption Expenditure Survey (CEX) Family-levelextracts by Harris and Sabelhaus (2000), available through the NBER website. We follow thevariable definitions in Harris and Sabelhaus (2000). The data contain observations of householdsof different cohorts taken at different points in time. Consumption is non-durables, defined as inHarris and Sabelhaus (2000). Stockholders are classified as households reporting ownership of stocks,bonds or mutual funds. Cohort age is defined as the age the household turns 25. The volatilityof consumption cohorts is computed as in Garleanu et al. (2012), but we restrict the sample tohouseholds that are shareholders. In the model, we measure consumption cohort effects by b(ωt).

Consumption growth of shareholders and non-shareholders are from Malloy et al. (2009) usingtheir definitions. We construct annualized growth rates using Dec-Dec growth, following Jagannathanand Wang (2007).

Stock returns

Firm stock return data are from CRSP. We form portfolios in June every year. We exclude financialfirms (SIC6000-6799), and utilities (SIC4900-4949). Data on the market portfolio and the risk-freerate are from Kenneth French’s website.

57